{"id":1772,"date":"2021-05-19T16:45:30","date_gmt":"2021-05-19T16:45:30","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math53\/chapter\/multiply-polynomials\/"},"modified":"2023-06-28T02:59:37","modified_gmt":"2023-06-28T02:59:37","slug":"multiply-polynomials","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math53\/chapter\/multiply-polynomials\/","title":{"raw":"6.2 Multiply Polynomials","rendered":"6.2 Multiply Polynomials"},"content":{"raw":"[latexpage]\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li>Multiply a polynomial by a monomial<\/li>\r\n \t<li>Multiply a binomial by a binomial<\/li>\r\n \t<li>Multiply a trinomial by a binomial<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<h1 data-type=\"title\">Multiply a Polynomial by a Monomial<\/h1>\r\n<p id=\"fs-id1169596306663\">We have used the Distributive Property to simplify expressions like \\(2\\left(x-3\\right)\\). You multiplied both terms in the parentheses, \\(x\\) and \\(3\\), by 2, to get \\(2x-6\\). With this chapter\u2019s new vocabulary, you can say you were multiplying a binomial, \\(x-3\\), by a monomial, 2<\/p>\r\n<p id=\"fs-id1169596291896\">Multiplying a <span class=\"no-emphasis\" data-type=\"term\">binomial<\/span> by a <span class=\"no-emphasis\" data-type=\"term\">monomial<\/span> is nothing new for you! Here\u2019s an example:<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596219597\" data-type=\"problem\">\r\n<p id=\"fs-id1169596367284\">Multiply: \\(4\\left(x+3\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596396832\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1172187674776\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the first row, the right column contains the expression 4 times x plus 3, with x plus 3 in parentheses. Two red arrows extend from 4, terminating at x and 3. In the second row, the text in the left column says \u201cDistribute.\u201d In the right column is 4 times x plus 4 times 3. In the last row, the text in the left column says \u201cSimplify.\u201d In the right column is 4x plus 12.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1172188943362\" data-type=\"media\" data-alt=\"4 times x plus 3. Two arrows extend from 4, terminating at x and 3.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/CNX_ElemAlg_Figure_06_03_001a_img_new.jpg\" alt=\"4 times x plus 3. Two arrows extend from 4, terminating at x and 3.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td><span id=\"eip-id1172189039404\" data-type=\"media\" data-alt=\"4 times x plus 4 times 3.\">[latex]4 {\\color{red}\\cdot} x + 4 {\\color{red}\\cdot} 3[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]4x+12[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596362495\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596235948\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596309264\" data-type=\"problem\">\r\n<p id=\"fs-id1169596274677\">Multiply: \\(5\\left(x+7\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596261412\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596295063\">\\(5x+35\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596360411\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596303507\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596238777\" data-type=\"problem\"><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596238777\" data-type=\"problem\">\r\n<p id=\"fs-id1169596317308\">Multiply: \\(3\\left(y+13\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596279454\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596319249\">\\(3y+39\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596360411\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596303507\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596279454\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596314988\" data-type=\"problem\">\r\n<p id=\"fs-id1169596309898\">Multiply: \\(y\\left(y-2\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596276390\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1172186802475\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the first row, the right column contains the expression y times y minus 2, with y minus 2 in parentheses. Two red arrows extend from the coefficient y, terminating at the y and minus 2 in parentheses. In the second row, the text in the left column says \u201cDistribute.\u201d In the right column is y times y minus y times 2. In the last row, the text in the left column says \u201cSimplify.\u201d In the right column is y squared minus 2y.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1172186802496\" data-type=\"media\" data-alt=\"y times y minus 2. Two arrows extend from the coefficient y, terminating at the y and minus 2 in parentheses.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_002a_img_new.jpg\" alt=\"y times y minus 2. Two arrows extend from the coefficient y, terminating at the y and minus 2 in parentheses.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td>[latex]y {\\color{red}\\cdot} y - y {\\color{red}\\cdot} 2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]y^2-2y[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596374530\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596370378\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596404931\" data-type=\"problem\">\r\n<p id=\"fs-id1169596255252\">Multiply: \\(x\\left(x-7\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596399324\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596370185\">\\({x}^{2}-7x\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596302246\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596377033\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596212720\" data-type=\"problem\"><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596212720\" data-type=\"problem\">\r\n<p id=\"fs-id1169596218283\">Multiply: \\(d\\left(d-11\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596344342\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596220091\">\\({d}^{2}-11d\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596302246\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596377033\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596344342\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596382289\" data-type=\"problem\">\r\n<p id=\"fs-id1169596310964\">Multiply: \\(7x\\left(2x+y\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596348801\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1172184496242\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the first row, the right column contains the expression yx times 2x plus y, with 2x plus y in parentheses. Two red arrows extend from 7x, terminating at 2x and y. In the second row, the text in the left column says \u201cDistribute.\u201d In the right column is 7x times 2x plus 7x times y. In the last row, the text in the left column says \u201cSimplify.\u201d In the right column is 14x squared plus 7xy.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1172184496262\" data-type=\"media\" data-alt=\"7 x times 2 x plus y. Two arrows extend from 7x, terminating at 2x and y.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_003a_img_new.jpg\" alt=\"7 x times 2 x plus y. Two arrows extend from 7x, terminating at 2x and y.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td>[latex]7x {\\color{red}\\cdot} 2x + 7x {\\color{red}\\cdot} y[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]14x^2 + 7xy[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596317227\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596367197\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596372008\" data-type=\"problem\">\r\n\r\nMultiply: \\(5x\\left(x+4y\\right)\\).\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596258487\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596370082\">\\(5{x}^{2}+20xy\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596367934\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596344668\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596393579\" data-type=\"problem\"><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596393579\" data-type=\"problem\">\r\n<p id=\"fs-id1169596557276\">Multiply: \\(2p\\left(6p+r\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596374505\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596240521\">\\(12{p}^{2}+2pr\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596367934\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596344668\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596374505\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596244318\" data-type=\"problem\">\r\n<p id=\"fs-id1169596375441\">Multiply: \\(-2y\\left(4{y}^{2}+3y-5\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596402073\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1172187836045\" class=\"unnumbered unstyled\" style=\"height: 84px\" summary=\"This figure has two columns. In the first row, the right column contains the expression negative 2y times 4y squared plus 3y minus 5, with 4y plus 3y minus 5 in parentheses. Three red arrows extend from negative 2y, terminating at 4y squared, 3y, and minus 5. In the second row, the text in the left column says \u201cDistribute.\u201d In the right column is negative 2y times 4y squared plus negative 2y times 3y minus negative 2y times 5. In the last row, the text in the left column says \u201cSimplify.\u201d In the right column is negative 8y cubed minus 6y squared plus 10y.\" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 48px\">\r\n<td style=\"height: 48px;width: 151.406px\"><\/td>\r\n<td style=\"height: 48px;width: 498.406px\"><span id=\"eip-id1172187836065\" data-type=\"media\" data-alt=\"Negative 2 y times 4 y squared plus 3 y minus 5. Three arrows extend from negative 2 y, terminating at 4 y squared, 3 y, and minus 5.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_004a_img_new.jpg\" alt=\"Negative 2 y times 4 y squared plus 3 y minus 5. Three arrows extend from negative 2 y, terminating at 4 y squared, 3 y, and minus 5.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px\">\r\n<td style=\"height: 18px;width: 151.406px\">Distribute.<\/td>\r\n<td style=\"height: 18px;width: 498.406px\"><span id=\"eip-id1172187836082\" data-type=\"media\" data-alt=\"Negative 2 y times 4 y squared plus negative 2 y times 3 y minus negative 2 y times 5.\">[latex]-2 y {\\color{red} \\cdot} 4 y^2+(-2 y) {\\color{red} \\cdot} 3 y-(-2 y) {\\color{red} \\cdot} 5[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px\">\r\n<td style=\"height: 18px;width: 151.406px\">Simplify.<\/td>\r\n<td style=\"height: 18px;width: 498.406px\">[latex]-8 y^3-6 y^2+10 y[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596287620\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596555903\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596298286\" data-type=\"problem\">\r\n<p id=\"fs-id1169596299296\">Multiply: \\(-3y\\left(5{y}^{2}+8y-7\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596307171\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596279480\">\\(-15{y}^{3}-24{y}^{2}+21y\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596318095\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596393126\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596338665\" data-type=\"problem\"><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596338665\" data-type=\"problem\">\r\n<p id=\"fs-id1169596396784\">Multiply: \\(4{x}^{2}\\left(2{x}^{2}-3x+5\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596288192\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596396920\">\\(8{x}^{4}-12{x}^{3}+20{x}^{2}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596318095\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596393126\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596288192\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596369884\" data-type=\"problem\">\r\n<p id=\"fs-id1169596382601\">Multiply: \\(2{x}^{3}\\left({x}^{2}-8x+1\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596369851\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1172187703559\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the first row, the right column contains the expression 2x cubed times x squared minus 8x plus 1, with x squared minus 8x plus 1 in parentheses. Three red arrows extend from 2x cubed, terminating at x squared, minus 8x, and 1. In the second row, the text in the left column says \u201cDistribute.\u201d In the right column is 2x cubed times x squared plus 2x cubed times negative 8x plus 2x cubed times 1. In the last row, the text in the left column says \u201cSimplify.\u201d In the right column is 2x to the fifth power minus 16x to the fourth power plus 2x cubed.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1172187703580\" data-type=\"media\" data-alt=\"2 x cubed times x squared minus 8 x plus 1. Three arrows extend from 2 x cubed, terminating at x squared, minus 8 x, and 1.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_005a_img_new.jpg\" alt=\"2 x cubed times x squared minus 8 x plus 1. Three arrows extend from 2 x cubed, terminating at x squared, minus 8 x, and 1.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td>[latex]2 x^3 {\\color{red} \\cdot} x^2+\\left(2 x^3\\right) {\\color{red} \\cdot}(-8 x)+\\left(2 x^3\\right) {\\color{red} \\cdot} 1[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]2 x^5-16 x^4+2 x^3[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596344336\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596291588\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596291590\" data-type=\"problem\">\r\n<p id=\"fs-id1169596308826\">Multiply: \\(4x\\left(3{x}^{2}-5x+3\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596279063\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596310312\">\\(12{x}^{3}-20{x}^{2}+12x\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596298449\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596397986\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596397988\" data-type=\"problem\"><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596397988\" data-type=\"problem\">\r\n<p id=\"fs-id1169596363190\">Multiply: \\(-6{a}^{3}\\left(3{a}^{2}-2a+6\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596292326\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596292328\">\\(-18{a}^{5}\\ + 12{a}^{4}-36{a}^{3}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596298449\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596397986\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596292326\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596372850\" data-type=\"problem\">\r\n<p id=\"fs-id1169596372852\">Multiply: \\(\\left(x+3\\right)p\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596302382\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1172182437666\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the first row, the text in the left column says \u201cThe monomial is the second factor.\u201d The right column contains the expression x plus 3, in parentheses, times p. Two red arrows extend from the p, terminating at x and 3. In the second row, the text in the left column says \u201cDistribute.\u201d In the right column is x times p plus 3 times p. In the last row, the text in the left column says \u201cSimplify.\u201d In the right column is xp plus 3p.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>The monomial is the second factor.<\/td>\r\n<td><span id=\"eip-id1172182437688\" data-type=\"media\" data-alt=\"x plus 3, in parentheses, times p. Two arrows extend from the p, terminating at x and 3.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_006a_img_new.jpg\" alt=\"x plus 3, in parentheses, times p. Two arrows extend from the p, terminating at x and 3.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td>[latex]x {\\color{red} \\cdot} p + 3{\\color{red} \\cdot} p[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]xp+3p[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596320183\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596315710\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596315712\" data-type=\"problem\">\r\n<p id=\"fs-id1169596315714\">Multiply: \\(\\left(x+8\\right)p\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596391243\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596391245\">\\(xp+8p\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596374701\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596374704\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596370491\" data-type=\"problem\"><\/div>\r\n<div id=\"fs-id1169596499263\" data-type=\"solution\">\r\n<p id=\"fs-id1169596285946\"><\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596370491\" data-type=\"problem\">\r\n<p id=\"fs-id1169596370493\">Multiply: \\(\\left(a+4\\right)p\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596499263\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596285946\">\\(ap+4p\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<h1 data-type=\"title\">Multiply a Binomial by a Binomial<\/h1>\r\n<p id=\"fs-id1169596303931\">Just like there are different ways to represent multiplication of numbers, there are several methods that can be used to multiply a <span class=\"no-emphasis\" data-type=\"term\">binomial<\/span> times a binomial. We will start by using the Distributive Property.<\/p>\r\n\r\n<h1 data-type=\"title\">Multiply a Binomial by a Binomial Using the Distributive Property<\/h1>\r\n<p id=\"fs-id1169596286032\">Look at the table below, where we multiplied a binomial by a <span class=\"no-emphasis\" data-type=\"term\">monomial<\/span>.<\/p>\r\n\r\n<table id=\"eip-id1172186695524\" class=\"grid\" summary=\"This figure has two columns. In the first row, the right column contains the expression x plus 3, in parentheses, times p. Two red arrows extend from the p, terminating at x and 3. In the second row, the text in the left column says \u201cWe distributed the p to get\u201d. The right column contains xp plus 3p. In the third row, the text in the left column says \u201cWhat if we have x plus 7 instead of p?\u201d In the right column is the product of two binomials, x plus 3 and x plus 7. Two red arrows extend from x plus 7, terminating at the x and the 3 in the first binomial. In the fourth row, the text in the left column says \u201cThink of the x plus 7 as the p above.\u201d In the right column is x times x plus 7 plus 3 times x plus 7, where x plus 7 is in parentheses twice. In the fifth row, the text in the left column says \u201cDistribute x plus 7.\u201d In the right column is x squared plus 7x plus 3x plus 21. In the sixth row, the text in the left column says \u201cCombine like terms.\u201d In the right column is x squared plus 10x plus 21.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1172186695544\" data-type=\"media\" data-alt=\"x plus 3, in parentheses, times p. Two arrows extend from the p, terminating at x and 3.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_007a_img_new.jpg\" alt=\"x plus 3, in parentheses, times p. Two arrows extend from the p, terminating at x and 3.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We distributed the <em data-effect=\"italics\">p<\/em> to get:<\/td>\r\n<td><span id=\"eip-id1172186695561\" data-type=\"media\" data-alt=\"x p plus 3 p.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_007b_img_new.jpg\" alt=\"x p plus 3 p.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>What if we have (<em data-effect=\"italics\">x<\/em> + 7) instead of <em data-effect=\"italics\">p<\/em>?<\/td>\r\n<td><span id=\"eip-id1172186695577\" data-type=\"media\" data-alt=\"x plus 3 multiplied by x plus 7. Two arrows extend from x plus 7, terminating at the x and the 3 in the first binomial.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_007c_img_new.jpg\" alt=\"x plus 3 multiplied by x plus 7. Two arrows extend from x plus 7, terminating at the x and the 3 in the first binomial.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute (<em data-effect=\"italics\">x<\/em> + 7).<\/td>\r\n<td><span id=\"eip-id1172182437009\" data-type=\"media\" data-alt=\"The sum of two products. The product of x and x plus 7, plus the product of 3 and x plus 7.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_007d_img_new.jpg\" alt=\"The sum of two products. The product of x and x plus 7, plus the product of 3 and x plus 7.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute again.<\/td>\r\n<td><span id=\"eip-id1172182437026\" data-type=\"media\" data-alt=\"x squared plus 7 x plus 3 x plus 21.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_007e_img_new.jpg\" alt=\"x squared plus 7 x plus 3 x plus 21.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td><span id=\"eip-id1172182437043\" data-type=\"media\" data-alt=\"x squared plus 10 x plus 21.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_007f_img_new.jpg\" alt=\"x squared plus 10 x plus 21.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1169596344846\">Notice that before combining like terms, you had four terms. You multiplied the two terms of the first binomial by the two terms of the second binomial\u2014four multiplications.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596458020\" data-type=\"problem\">\r\n<p id=\"fs-id1169596458022\">Multiply: \\(\\left(y+5\\right)\\left(y+8\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596308212\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1172185589112\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the first row, the right column contains the product of two binomials, y plus 5 and y plus 8. Two arrows extend from y plus 8, terminating at the y and 5 in the first binomial. In the second row, the text in the left column says \u201cDistribute y plus 8.\u201d The right column contains y times y plus 8 plus 5 times y plus 8, where y plus 8 is in parentheses twice. In the third row, the text in the left column says \u201cDistribute again.\u201d In the right column is y squared plus 8y plus 5y plus 40. In the last row, the text in the left column says \u201cCombine like terms.\u201d In the right column is y squared plus 13y plus 40.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1172187708587\" data-type=\"media\" data-alt=\"The product of two binomials, y plus 5 and y plus 8. Two arrows extend from y plus 8, terminating at the y and the 5 in the first binomial.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_008a_img_new.jpg\" alt=\"The product of two binomials, y plus 5 and y plus 8. Two arrows extend from y plus 8, terminating at the y and the 5 in the first binomial.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute (<em data-effect=\"italics\">y<\/em> + 8).<\/td>\r\n<td><span id=\"eip-id1172187708604\" data-type=\"media\" data-alt=\"The sum of two products, the product of y and y plus 8, plus the product of 5 and y plus 8.\">[latex]y {\\color{red}{(y+8)}}+5{\\color{red}{(y+8)}}[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute again<\/td>\r\n<td>[latex]y {\\color{red}{\\cdot}} y +y {\\color{red}{\\cdot}} 8 + 5 {\\color{red}{\\cdot}} y + 5 {\\color{red}{\\cdot}} 8[\/latex]\r\n\r\n[latex]y^2+8 y+5 y+40[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>[latex]y^2+13 y+40[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nMultiply: \\(\\left(x+8\\right)\\left(x+9\\right)\\).\r\n<div id=\"fs-id1169596291728\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596291732\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596499248\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596499251\">\\({x}^{2}+17x+72\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596360795\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596360798\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596360800\" data-type=\"problem\"><\/div>\r\n<div id=\"fs-id1169596375449\" data-type=\"solution\">\r\n<p id=\"fs-id1169596348525\"><\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596360800\" data-type=\"problem\">\r\n<p id=\"fs-id1169596366221\">Multiply: \\(\\left(5x+9\\right)\\left(4x+3\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596375449\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596348525\">\\(20{x}^{2}+51x+27\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596360795\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596360798\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596375449\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596402877\" data-type=\"problem\">\r\n<p id=\"fs-id1169596402879\">Multiply: \\(\\left(2y+5\\right)\\left(3y+4\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596303688\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1172187825290\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the first row, the right column contains the product of two binomials, 2y plus 5 and 3y plus 4. Two arrows extend from 3y plus 4, terminating at 2y and 5 in the first binomial. In the second row, the text in the left column says \u201cDistribute 3y plus 4.\u201d The right column contains 2y times 3y plus 4 plus 5 times 3y plus 4, where 3y plus 4 is in parentheses twice. In the third row, the text in the left column says \u201cDistribute again.\u201d In the right column is 6y squared plus 8y plus 15y plus 20. In the last row, the text in the left column says \u201cCombine like terms.\u201d In the right column is 6y squared plus 23y plus 20.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1172187825310\" data-type=\"media\" data-alt=\"The product of two binomials, 2 y plus 5 and 3 y plus 4. Two arrows extend from 3y plus 4, terminating at 2y and 5 in the first binomial.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_009a_img_new.jpg\" alt=\"The product of two binomials, 2 y plus 5 and 3 y plus 4. Two arrows extend from 3y plus 4, terminating at 2y and 5 in the first binomial.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute (3<em data-effect=\"italics\">y<\/em> + 4).<\/td>\r\n<td>[latex]2 y {\\color{red}(3 y+4)}+5 {\\color{red}(3 y+4)}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute again<\/td>\r\n<td>[latex]2y {\\color{red}{\\cdot}} 3y + 2y {\\color{red}{\\cdot}} 4 + 5 {\\color{red}{\\cdot}} 3y + 5 {\\color{red}{\\cdot}} 4[\/latex]\r\n\r\n[latex]6 y^2+8 y+15 y+20[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>[latex]6 y^2+23 y+20[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596286465\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596286279\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596286281\" data-type=\"problem\">\r\n<p id=\"fs-id1169596286284\">Multiply: \\(\\left(3b+5\\right)\\left(4b+6\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596286011\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596286013\">\\(12{b}^{2}+38b+30\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596286306\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596286309\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596286311\" data-type=\"problem\"><\/div>\r\n<div id=\"fs-id1169596374723\" data-type=\"solution\">\r\n<p id=\"fs-id1169596285411\"><\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596286311\" data-type=\"problem\">\r\n<p id=\"fs-id1169596286755\">Multiply: \\(\\left(a+10\\right)\\left(a+7\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596374723\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596285411\">\\({a}^{2}+17a+70\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596286306\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596286309\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596374723\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"problem\">\r\n<p id=\"fs-id1169596367035\">Multiply: \\(\\left(4y+3\\right)\\left(2y-5\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596360324\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1172181066482\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the first row, the right column contains the product of two binomials, 4y plus 3 and 2y minus 5. Two arrows extend from 2y minus 5, terminating at 4y and 3 in the first binomial. In the second row, the text in the left column says \u201cDistribute.\u201d The right column contains 4y times 2y minus 5 plus 3 times 2y minus 5, where 2y minus 5 is in parentheses twice. In the third row, the text in the left column says \u201cDistribute again.\u201d In the right column is 8y squared minus 20y plus 6y minus 15. In the last row, the text in the left column says \u201cCombine like terms.\u201d In the right column is 8y squared minus 14y minus 15.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1172181066502\" data-type=\"media\" data-alt=\"The product of two binomials, 4y plus 3 and 2 y minus 5. Two arrows extend from 2y minus 5, terminating at 4 y and 3 in the first binomial.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_010a_img_new.jpg\" alt=\"The product of two binomials, 4y plus 3 and 2 y minus 5. Two arrows extend from 2y minus 5, terminating at 4 y and 3 in the first binomial.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td>[latex]4 y {\\color{red}{(2 y-5)}}+3{\\color{red}{(2 y-5)}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute again.<\/td>\r\n<td>[latex]4y {\\color{red}{\\cdot}} 2y + 4y {\\color{red}{\\cdot}} (-5) + 3 {\\color{red}{\\cdot}} 2y + 3 {\\color{red}{\\cdot}} (-5)[\/latex]\r\n\r\n[latex]8 y^2-20 y+6 y-15[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>[latex]8 y^2-14 y-15[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596386394\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596348839\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596348842\" data-type=\"problem\">\r\n<p id=\"fs-id1169596348844\">Multiply: \\(\\left(5y+2\\right)\\left(6y-3\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596391031\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596401314\">\\(30{y}^{2}-3y-6\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596392758\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596392762\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596360936\" data-type=\"problem\"><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596360936\" data-type=\"problem\">\r\n<p id=\"fs-id1169596360938\">Multiply: \\(\\left(3c+4\\right)\\left(5c-2\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596397978\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596397980\">\\(15{c}^{2}+14c-8\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596392758\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596392762\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596397978\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596401560\" data-type=\"problem\">\r\n<p id=\"fs-id1169596401562\">Multiply: \\(\\left(x+2\\right)\\left(x-y\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596378360\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1172182438454\" class=\"unnumbered unstyled\" style=\"height: 90px\" summary=\"This figure has two columns. In the first row, the right column contains the product of two binomials, x minus 2 and x minus y. Two arrows extend from x minus y, terminating at x and 2 in the first binomial. In the second row, the text in the left column says \u201cDistribute.\u201d The right column contains x times x minus y minus 2 times x minus y, where x minus y is in parentheses twice. In the third row, the text in the left column says \u201cDistribute again.\u201d In the right column is x squared minus xy minus 2x plus 2y. In the last row, the text in the left column says \u201cThere are no like terms to combine.\u201d\" width=\"100%\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1172182438474\" data-type=\"media\" data-alt=\"The product of two binomials, x minus 2 and x minus y. Two arrows extend from x minus y, terminating at x and 2 in the first binomial.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_011a_img_new.jpg\" alt=\"The product of two binomials, x minus 2 and x minus y. Two arrows extend from x minus y, terminating at x and 2 in the first binomial.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td>[latex]x {\\color{red}{(x-y)}}-2{\\color{red}{(x-y)}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute again.<\/td>\r\n<td>[latex]x {\\color{red}{\\cdot}} (x) + x {\\color{red}{\\cdot}} (-y) + (-2) {\\color{red}{\\cdot}} (x) + (-2) {\\color{red}{\\cdot}} (-y)[\/latex]\r\n\r\n[latex]x^2-x y-2 x+2 y[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>There are no like terms to combine.<\/td>\r\n<td>[latex]x^2-x y-2 x+2 y[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596375029\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596375033\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596375035\" data-type=\"problem\">\r\n<p id=\"fs-id1169596375037\">Multiply: \\(\\left(a+7\\right)\\left(a-b\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596373985\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596373987\">\\({a}^{2}-ab+7a-7b\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596384881\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596393617\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596393619\" data-type=\"problem\"><\/div>\r\n<div id=\"fs-id1169596398460\" data-type=\"solution\">\r\n<p id=\"fs-id1169596558190\"><\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596393619\" data-type=\"problem\">\r\n<p id=\"fs-id1169596393621\">Multiply: \\(\\left(x+5\\right)\\left(x-y\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596398460\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596558190\">\\({x}^{2}-xy+5x-5y\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1 data-type=\"title\">Multiply a Binomial by a Binomial Using the FOIL Method<\/h1>\r\n<p id=\"fs-id1169596308783\">Remember that when you multiply a binomial by a binomial you get four terms. Sometimes you can combine like terms to get a <span class=\"no-emphasis\" data-type=\"term\">trinomial<\/span>, but sometimes, like in the above example, there are no like terms to combine.<\/p>\r\n<p id=\"fs-id1169596556140\">Let\u2019s look at the last example again and pay particular attention to how we got the four terms.<\/p>\r\n\r\n<div id=\"fs-id1169596556146\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{c}\\hfill \\left(x-2\\right)\\left(x-y\\right)\\hfill \\\\ \\hfill {x}^{2}-xy-2x+2y\\hfill \\end{array}\\)<\/div>\r\n<p id=\"fs-id1169596388950\">Where did the first term, \\({x}^{2}\\), come from?<\/p>\r\n<span id=\"fs-id1169596298873\" data-type=\"media\" data-alt=\"This figure explains how to multiply a binomial using the FOIL method. It has two columns, with written instructions on the left and math on the right. At the top of the figure, the text in the left column says \u201cIt is the product of x and x, the first terms in x minus 2 and x minus y.\u201d In the right column is the product of x minus 2 and x minus y. An arrow extends from the x in x minus 2, and terminates at the x in x minus y. Below this is the word \u201cFirst.\u201d One row down, the text in the left column says \u201cThe next terms, negative xy, is the product of x and negative y, the two outer terms.\u201d In the right column is the product of x minus 2 and x minus y, with another arrow extending from the x in x minus 2 to the y in x minus y. Below this is the word \u201cOuter.\u201d One row down, the text in the left column says \u201cThe third term, negative 2 x, is the product of negative 2 and x, the two inner terms.\u201d In the right column is the product of x minus 2 and x minus y with a third arrow extending from minus 2 in x minus 2 and terminating at the x in x minus y. Below this is the word \u201cInner.\u201d In the last row, the text in the left column says \u201cAnd the last term, plus 2y, came from multiplying the two last terms, negative 2 and negative y.\u201d In the right column is the product of x minus 2 and x minus y, with a fourth arrow extending from the minus 2 in x minus 2 to the minus y in x minus y. Below this is the word \u201cLast.\u201d\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_012_img_new.jpg\" alt=\"This figure explains how to multiply a binomial using the FOIL method. It has two columns, with written instructions on the left and math on the right. At the top of the figure, the text in the left column says \u201cIt is the product of x and x, the first terms in x minus 2 and x minus y.\u201d In the right column is the product of x minus 2 and x minus y. An arrow extends from the x in x minus 2, and terminates at the x in x minus y. Below this is the word \u201cFirst.\u201d One row down, the text in the left column says \u201cThe next terms, negative xy, is the product of x and negative y, the two outer terms.\u201d In the right column is the product of x minus 2 and x minus y, with another arrow extending from the x in x minus 2 to the y in x minus y. Below this is the word \u201cOuter.\u201d One row down, the text in the left column says \u201cThe third term, negative 2 x, is the product of negative 2 and x, the two inner terms.\u201d In the right column is the product of x minus 2 and x minus y with a third arrow extending from minus 2 in x minus 2 and terminating at the x in x minus y. Below this is the word \u201cInner.\u201d In the last row, the text in the left column says \u201cAnd the last term, plus 2y, came from multiplying the two last terms, negative 2 and negative y.\u201d In the right column is the product of x minus 2 and x minus y, with a fourth arrow extending from the minus 2 in x minus 2 to the minus y in x minus y. Below this is the word \u201cLast.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1169596497182\">We abbreviate \u201cFirst, Outer, Inner, Last\u201d as FOIL. The letters stand for \u2018<strong data-effect=\"bold\">F<\/strong>irst, <strong data-effect=\"bold\">O<\/strong>uter, <strong data-effect=\"bold\">I<\/strong>nner, <strong data-effect=\"bold\">L<\/strong>ast\u2019. The word FOIL is easy to remember and ensures we find all four products.\r\n<img class=\"size-medium wp-image-2040 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/FOIL-300x142.png\" alt=\"FOIL image\" width=\"300\" height=\"142\" \/><\/p>\r\n\\((x-2)(x-y)\\)\r\n\r\n\\(\\begin{matrix}{x}^{2}- xy- 2x+ 2y \\\\ F \\quad \\enspace O \\quad \\enspace I \\quad \\enspace L \\end{matrix}\\)\r\n<p id=\"fs-id1169596308801\">Let\u2019s look at \\(\\left(x+3\\right)\\left(x+7\\right)\\).<\/p>\r\n\r\n<table id=\"eip-id1172181067051\" class=\"grid\" summary=\"This figure compares using the distributive property to using the FOIL method for multiplying the binomials x plus 3 and x plus 7. The figure has two columns. Written at the top of the left column is \u201cDistributive Property. Below this is the product of x plus 3 and x plus 7. Below this is x times x plus 7 plus 3 times x plus 7, where x plus 7 is in parentheses twice. Below this is x squared plus 7x plus 3x plus 21. Below x squared is the letter F, below 7x is the letter O, below 3x is the letter I, and below 21 is the letter L, spelling FOIL. Below this is the expression with like terms combined: x squared plus 10x plus 21. Written at the top of the right column is \u201cFOIL.\u201d Below this is the product of x plus 3 and x plus y. An arrow extends from the x in x plus 3 to the x in x plus 7. A second arrow extends from the x in x plus 3 to the 7 in x plus 7. A third arrow extends from the 3 in x plus 3 to the x in x plus 7. A fourth arrow extends from the 3 in x plus 3 to the 7 in x plus 7. Below this is the same expression arrived at through the distributive property in the left column: x squared plus 7x plus 3x plus 21, with the letter F below x squared, the letter O below 7x, the letter I below 3x, and the letter L below 21. Below this is the expression with like terms combined once more: x squared plus 10x plus 21.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td data-align=\"center\">Distibutive Property<\/td>\r\n<td data-align=\"center\">FOIL<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span id=\"eip-id1172181067077\" data-type=\"media\" data-alt=\"The product of x plus 3 and x plus 7.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_022a_img_new.jpg\" alt=\"The product of x plus 3 and x plus 7.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<td><span id=\"eip-id1172181067088\" data-type=\"media\" data-alt=\"The product of x plus 3 and x plus y. An arrow extends from the x in x plus 3 to the x in x plus 7. A second arrow extends from the x in x plus 3 to the 7 in x plus 7. A third arrow extends from the 3 in x plus 3 to the x in x plus 7. A fourth arrow extends from the 3 in x plus 3 to the 7 in x plus 7.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_022e_img_new.jpg\" alt=\"The product of x plus 3 and x plus y. An arrow extends from the x in x plus 3 to the x in x plus 7. A second arrow extends from the x in x plus 3 to the 7 in x plus 7. A third arrow extends from the 3 in x plus 3 to the x in x plus 7. A fourth arrow extends from the 3 in x plus 3 to the 7 in x plus 7.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span id=\"eip-id1172181067102\" data-type=\"media\" data-alt=\"The sum of two products, the product of x and x plus 7, and the product of 3 and x plus 7.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_022b_img_new.jpg\" alt=\"The sum of two products, the product of x and x plus 7, and the product of 3 and x plus 7.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span id=\"eip-id1172181067118\" data-type=\"media\" data-alt=\"x squared plus 7 x plus 3 x plus 21. Below x squared is the letter F, below 7 x is the letter O, below 3 x is the letter I, and below 21 is the letter L, spelling FOIL.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_022c_img_new.jpg\" alt=\"x squared plus 7 x plus 3 x plus 21. Below x squared is the letter F, below 7 x is the letter O, below 3 x is the letter I, and below 21 is the letter L, spelling FOIL.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<td><span id=\"eip-id1172181067128\" data-type=\"media\" data-alt=\"x squared plus 7 x plus 3 x plus 21. Below x squared is the letter F, below 7 x is the letter O, below 3 x is the letter I, and below 21 is the letter L, spelling FOIL.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_022f_img_new.jpg\" alt=\"x squared plus 7 x plus 3 x plus 21. Below x squared is the letter F, below 7 x is the letter O, below 3 x is the letter I, and below 21 is the letter L, spelling FOIL.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span id=\"eip-id1172181067142\" data-type=\"media\" data-alt=\"x squared plus 10 x plus 21.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_022d_img_new.jpg\" alt=\"x squared plus 10 x plus 21.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<td><span id=\"eip-id1172181067153\" data-type=\"media\" data-alt=\"x squared plus 10 x plus 21.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_022g_img_new.jpg\" alt=\"x squared plus 10 x plus 21.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1169596376847\">Notice how the terms in third line fit the FOIL pattern.<\/p>\r\n<p id=\"fs-id1169596376850\">Now we will do an example where we use the FOIL pattern to multiply two binomials.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"title\">How to Multiply a Binomial by a Binomial using the FOIL Method<\/div>\r\n<div id=\"fs-id1169596376856\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596276394\" data-type=\"problem\">\r\n<p id=\"fs-id1169596276399\">Multiply using the FOIL method: \\(\\left(x+5\\right)\\left(x+9\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596361161\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solutio<\/strong><strong>n<\/strong><\/div>\r\n<div data-type=\"title\">\r\n<table style=\"border-collapse: collapse;width: 100%;height: 274px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 101.325%;height: 16px;text-align: center\" colspan=\"3\">\\(\\left(x+5\\right)\\left(x+9\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 54px\">\r\n<td style=\"width: 36.9258%;height: 54px\"><strong>Step 1.<\/strong>\r\nMultiply the <em data-effect=\"italics\"><span style=\"color: #ff0000\">First<\/span>\u00a0<\/em>terms, [latex]\\color{red} x \\cdot x [\/latex]<\/td>\r\n<td style=\"width: 16.4312%;height: 54px\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_1.jpg\"><img class=\"alignnone wp-image-2685\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_1.jpg\" alt=\"the product of binomials x plus 5 and x plus 9. Below this is the product of x plus 5 and x plus 9 again, with an arrow extending from the x in the first binomial to the x in the second binomial.\" width=\"110\" height=\"53\" \/><\/a><\/td>\r\n<td style=\"width: 47.9682%;height: 54px\">\r\n<p style=\"text-align: center\">[latex] \\begin{array}{ccccccc} {\\color{red}{x^2}} &amp; + &amp; \\rule{.5cm}{0.4pt} &amp;\r\n+ &amp; \\rule{.5cm}{0.4pt} &amp; + &amp; \\rule{.5cm}{0.4pt} \\\\ F &amp; &amp; O &amp; &amp; I &amp; &amp; L \\\\ \\end{array} [\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr style=\"height: 54px\">\r\n<td style=\"width: 36.9258%;height: 54px\"><strong>Step 2.<\/strong>\r\nMultiply the <em data-effect=\"italics\"><span style=\"color: #ff0000\">Outer<\/span>\u00a0<\/em>terms, [latex]\\color{red} x \\cdot 9 [\/latex]<\/td>\r\n<td style=\"width: 16.4312%;height: 54px\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_2.jpg\"><img class=\"alignnone wp-image-2686\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_2.jpg\" alt=\"the product of x plus 5 and x plus 9 again, with an arrow extending from x in the first binomial to the 9 in the second binomial.\" width=\"110\" height=\"41\" \/><\/a><\/td>\r\n<td style=\"width: 47.9682%;height: 54px;text-align: center\">[latex]\\begin{array}{ccccccc} x^2 &amp; {\\color{red}{+}} &amp;{\\color{red}{9x}} &amp;\r\n+ &amp; \\rule{.5cm}{0.4pt} &amp; + &amp; \\rule{.5cm}{0.4pt} \\\\ F &amp; &amp; O &amp; &amp; I &amp; &amp; L \\\\ \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 66px\">\r\n<td style=\"width: 36.9258%;height: 66px\"><strong>Step 3.<\/strong>\r\nMultiply the <span style=\"color: #ff0000\"><em data-effect=\"italics\">Inner <\/em><\/span>terms, [latex]\\color{red} 5 \\cdot x [\/latex]<\/td>\r\n<td style=\"width: 16.4312%;height: 66px\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_3.jpg\"><img class=\"alignnone wp-image-2687\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_3.jpg\" alt=\"contains the product of x plus 5 and x plus 9 again, with an arrow extending from 5 in the first binomial to the x in the second binomial. \" width=\"110\" height=\"39\" \/><\/a><\/td>\r\n<td style=\"width: 47.9682%;height: 66px;text-align: center\">[latex]\\begin{array}{ccccccc} x^2 &amp; + &amp; 9x &amp;\r\n+ &amp; {\\color{red}{5x}} &amp; + &amp; \\rule{.5cm}{0.4pt} \\\\ F &amp; &amp; O &amp; &amp; I &amp; &amp; L \\\\ \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 68px\">\r\n<td style=\"width: 36.9258%;height: 68px\"><strong>Step 4.<\/strong>\r\nMultiply the<span style=\"color: #ff0000\"> <em data-effect=\"italics\">Last <\/em><\/span>terms, [latex]\\color{red} 5 \\cdot 9 [\/latex]<\/td>\r\n<td style=\"width: 16.4312%;height: 68px\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_4.jpg\"><img class=\"alignnone wp-image-2688\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_4.jpg\" alt=\" the product of x plus 5 and x plus 9 again, with an arrow extending from 5 in the first binomial to 9 in the second binomial.\" width=\"110\" height=\"46\" \/><\/a><\/td>\r\n<td style=\"width: 47.9682%;height: 68px;text-align: center\">[latex]\\begin{array}{ccccccc} x^2 &amp; + &amp; 9x &amp;\r\n+ &amp; 5x &amp; {\\color{red}{+}}&amp; {\\color{red}{45}} \\\\ F &amp; &amp; O &amp; &amp; I &amp; &amp; L \\\\ \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 36.9258%;height: 16px\"><strong>Step 5.<\/strong> Combine like terms.<\/td>\r\n<td style=\"width: 16.4312%;height: 16px\"><\/td>\r\n<td style=\"width: 47.9682%;height: 16px;text-align: center\">[latex]x^2+14x+45[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596398431\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596398435\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596398437\" data-type=\"problem\">\r\n<p id=\"fs-id1169596398439\">Multiply using the FOIL method: \\(\\left(x+6\\right)\\left(x+8\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596360980\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596360982\">\\({x}^{2}+14x+48\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596405489\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596405493\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596405495\" data-type=\"problem\"><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596405495\" data-type=\"problem\">\r\n<p id=\"fs-id1169596405497\">Multiply using the FOIL method: \\(\\left(y+17\\right)\\left(y+3\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596364325\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596364327\">\\({y}^{2}+20y+51\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\nWe summarize the steps of the FOIL method below. The FOIL method only applies to multiplying binomials, not other polynomials!\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Multiply two binomials using the FOIL method<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n<span id=\"fs-id1171792521436\" data-type=\"media\" data-alt=\".\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_026_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169596450761\">When you multiply by the FOIL method, drawing the lines will help your brain focus on the pattern and make it easier to apply.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596450770\" data-type=\"problem\">\r\n<p id=\"fs-id1169596450772\">Multiply: \\(\\left(y-7\\right)\\left(y+4\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596365991\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\">\r\n<table style=\"border-collapse: collapse;width: 100%;height: 274px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 101.325%;height: 16px;text-align: right\" colspan=\"3\">\\(\\left(y-7\\right)\\left(y+4\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 54px\">\r\n<td style=\"width: 36.9258%;height: 54px\">Multiply the <em data-effect=\"italics\"><span style=\"color: #ff0000\">First<\/span>\u00a0<\/em>terms, [latex]\\color{red} y \\cdot y [\/latex]<\/td>\r\n<td style=\"width: 16.4312%;height: 54px\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_1.jpg\"><img class=\"alignnone wp-image-2678\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_1.jpg\" alt=\"This image shows the product of two binomials, y minus 7 and y plus 4, with an arrow extending from the y in the first binomial to the y in the second binomial.\" width=\"110\" height=\"44\" \/><\/a><\/td>\r\n<td style=\"width: 47.9682%;height: 54px\">\r\n<p style=\"text-align: center\">[latex] \\begin{array}{ccccccc} {\\color{red}{y^2}} &amp; + &amp; \\rule{.5cm}{0.4pt} &amp;\r\n+ &amp; \\rule{.5cm}{0.4pt} &amp; + &amp; \\rule{.5cm}{0.4pt} \\\\ F &amp; &amp; O &amp; &amp; I &amp; &amp; L \\\\ \\end{array} [\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr style=\"height: 54px\">\r\n<td style=\"width: 36.9258%;height: 54px\">Multiply the <em data-effect=\"italics\"><span style=\"color: #ff0000\">Outer<\/span>\u00a0<\/em>terms, [latex]\\color{red} y \\cdot 4 [\/latex]<\/td>\r\n<td style=\"width: 16.4312%;height: 54px\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_2.jpg\"><img class=\"alignnone wp-image-2679\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_2.jpg\" alt=\"This image shows the product of y minus 7 and y plus 4 again, with a second arrow extending from y in the first binomial to 4 in the second binomial.\" width=\"110\" height=\"55\" \/><\/a><\/td>\r\n<td style=\"width: 47.9682%;height: 54px;text-align: center\">[latex]\\begin{array}{ccccccc} y^2 &amp; {\\color{red}{+}} &amp;{\\color{red}{4y}} &amp;\r\n+ &amp; \\rule{.5cm}{0.4pt} &amp; + &amp; \\rule{.5cm}{0.4pt} \\\\ F &amp; &amp; O &amp; &amp; I &amp; &amp; L \\\\ \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 66px\">\r\n<td style=\"width: 36.9258%;height: 66px\">Multiply the <span style=\"color: #ff0000\"><em data-effect=\"italics\">Inner <\/em><\/span>terms, [latex]\\color{red} -7 \\cdot y [\/latex]<\/td>\r\n<td style=\"width: 16.4312%;height: 66px\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_3.jpg\"><img class=\"alignnone wp-image-2680\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_3.jpg\" alt=\"This image shows the product of y minus 7 and y plus 4 again, with a third arrow extending from the minus 7 in the first binomial to the y in the second binomial.\" width=\"110\" height=\"71\" \/><\/a><\/td>\r\n<td style=\"width: 47.9682%;height: 66px;text-align: center\">[latex]\\begin{array}{ccccccc} y^2 &amp; + &amp; 4y &amp;\r\n{\\color{red}{-}} &amp; {\\color{red}{7y}} &amp; + &amp; \\rule{.5cm}{0.4pt} \\\\ F &amp; &amp; O &amp; &amp; I &amp; &amp; L \\\\ \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 68px\">\r\n<td style=\"width: 36.9258%;height: 68px\">Multiply the<span style=\"color: #ff0000\"> <em data-effect=\"italics\">Last <\/em><\/span>terms, [latex]\\color{red} -7 \\cdot 4 [\/latex]<\/td>\r\n<td style=\"width: 16.4312%;height: 68px\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_4.jpg\"><img class=\"alignnone wp-image-2681\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_4.jpg\" alt=\"This image shows the product of y minus 7 and y plus 4 again, with a fourth arrow extending from minus 7 in the first binomial to 4 in the second binomial.\" width=\"110\" height=\"74\" \/><\/a><\/td>\r\n<td style=\"width: 47.9682%;height: 68px;text-align: center\">[latex]\\begin{array}{ccccccc} y^2 &amp; + &amp; 4y &amp;\r\n- &amp; 7y &amp; {\\color{red}{-}}&amp; {\\color{red}{28}} \\\\ F &amp; &amp; O &amp; &amp; I &amp; &amp; L \\\\ \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 36.9258%;height: 16px\">Combine like terms.<\/td>\r\n<td style=\"width: 16.4312%;height: 16px\"><\/td>\r\n<td style=\"width: 47.9682%;height: 16px;text-align: center\">[latex]y^2-3y-28[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596360918\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596360922\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596360925\" data-type=\"problem\">\r\n<p id=\"fs-id1169596360927\">Multiply: \\(\\left(x-7\\right)\\left(x+5\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596299632\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596299634\">\\({x}^{2}-2x-35\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596376719\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596376723\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596376725\" data-type=\"problem\"><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596376725\" data-type=\"problem\">\r\n<p id=\"fs-id1169596557706\">Multiply: \\(\\left(b-3\\right)\\left(b+6\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596499681\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596499684\">\\({b}^{2}+3b-18\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596376719\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596376723\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596499681\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596374507\" data-type=\"problem\">\r\n<p id=\"fs-id1169596374509\">Multiply: \\(\\left(4x+3\\right)\\left(2x-5\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596558267\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\">\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">\\(\\left(4x+3\\right)\\left(2x-5\\right)\\)<\/td>\r\n<td style=\"width: 50%\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Screenshot-2023-06-27-190936.jpg\"><img class=\"alignnone wp-image-2676\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Screenshot-2023-06-27-190936.jpg\" alt=\"\" width=\"126\" height=\"77\" \/><\/a><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Multiply the <em data-effect=\"italics\"><span style=\"color: #ff0000\">First<\/span>\u00a0<\/em>terms, [latex]\\color{red} 4x \\cdot 2x[\/latex]<\/td>\r\n<td style=\"width: 50%\">\r\n<p style=\"text-align: left\">[latex] \\begin{array}{ccccccc} {\\color{red}{8x^2}} &amp; + &amp; \\rule{.5cm}{0.4pt} &amp;\r\n+ &amp; \\rule{.5cm}{0.4pt} &amp; + &amp; \\rule{.5cm}{0.4pt} \\\\ F &amp; &amp; O &amp; &amp; I &amp; &amp; L \\\\ \\end{array} [\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Multiply the <em data-effect=\"italics\"><span style=\"color: #ff0000\">Outer<\/span>\u00a0<\/em>terms, [latex]\\color{red} 4x \\cdot (-5)[\/latex]<\/td>\r\n<td style=\"width: 50%\">[latex]\\begin{array}{ccccccc} 8x^2 &amp; {\\color{red}{-}} &amp;{\\color{red}{20x}} &amp;\r\n+ &amp; \\rule{.5cm}{0.4pt} &amp; + &amp; \\rule{.5cm}{0.4pt} \\\\ F &amp; &amp; O &amp; &amp; I &amp; &amp; L \\\\ \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Multiply the <span style=\"color: #ff0000\"><em data-effect=\"italics\">Inner <\/em><\/span>terms, [latex]\\color{red} 3 \\cdot 2x [\/latex]<\/td>\r\n<td style=\"width: 50%\">[latex]\\begin{array}{ccccccc} 8x^2 &amp; - &amp; 20x &amp;\r\n{\\color{red}{+}} &amp; {\\color{red}{6x}} &amp; + &amp; \\rule{.5cm}{0.4pt} \\\\ F &amp; &amp; O &amp; &amp; I &amp; &amp; L \\\\ \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Multiply the<span style=\"color: #ff0000\"> <em data-effect=\"italics\">Last <\/em><\/span>terms, [latex]\\color{red} 3 \\cdot (-5)[\/latex]<\/td>\r\n<td style=\"width: 50%\">[latex]\\begin{array}{ccccccc} 8x^2 &amp; - &amp;20x &amp;\r\n+ &amp; 6x &amp; {\\color{red}{-}}&amp; {\\color{red}{15}} \\\\ F &amp; &amp; O &amp; &amp; I &amp; &amp; L \\\\ \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">Combine like terms.<\/td>\r\n<td style=\"width: 50%\">[latex]8x^2-14x-15[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596387847\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596455638\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596455640\" data-type=\"problem\">\r\n<p id=\"fs-id1169596455642\">Multiply: \\(\\left(3x+7\\right)\\left(5x-2\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596310554\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596310556\">\\(15{x}^{2}+29x-14\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596389245\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596389248\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596389250\" data-type=\"problem\"><\/div>\r\n<div id=\"fs-id1169596367182\" data-type=\"solution\">\r\n<p id=\"fs-id1169596557998\"><\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596389250\" data-type=\"problem\">\r\n<p id=\"fs-id1169596389252\">Multiply: \\(\\left(4y+5\\right)\\left(4y-10\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596367182\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596557998\">\\(16{y}^{2}-20y-50\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169596558024\">The final products in the last four examples were trinomials because we could combine the two middle terms. This is not always the case.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"eip-id1172187806128\" data-type=\"problem\">\r\n<p id=\"eip-id1172187806130\">Multiply: \\(\\left(3x-y\\right)\\left(2x-5\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"eip-id1172187806134\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1172187806137\" class=\"unnumbered unstyled\" style=\"width: 100%\" summary=\"This figure has three columns. At the top of the figure, the second column contains the product of two binomials, 3x minus y and 2x minus 5. One row down, the text in the first column says \u201cMultiply the first terms.\u201d The second column contains 6x squared plus blank plus blank plus blank. Beneath 6x squared is the letter F and beneath each blank are the letters O, I, and L, respectively. One row down, the text in the first column says \u201cMultiply the outer terms.\u201d The second column contains 6x squared minus 15x plus blank plus blank. Below 6x squared is F, below 15x is O, and below the blanks are I and L. One row down, the text in the first column says \u201cMultiply the inner terms.\u201d The second column contains 6x squared minus 15x minus 2xy plus blank. One row down, the text in the first column says \u201cMultiply the last terms.\u201d The second column contains the full expression, 6x squared minus 15x minus 2xy plus 5y, with each letter of FOIL beneath each of the terms. At the bottom of the image, the text in the first column says \u201cCombine like terms\u2014there are none.\u201d In the right column is 6x squared minus 15x minus 2xy plus 5y. In the third column is the product of the two binomials again, 3x minus y times 2x minus 5. An arrow extends from 3x in the first binomial to 2x in the second binomial. A second arrow extends from 3x in the first binomial to minus 5 in the second binomial. A third arrow extends from y in the first binomial to 2x in the second binomial. A fourth arrow extends from y in the first binomial to minus 5 in the second binomial.\" width=\"100%\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 44.0812%\">\\(\\left(3x-y\\right)\\left(2x-5\\right)\\)<\/td>\r\n<td style=\"width: 55.8304%\"><span id=\"eip-id1172187806172\" data-type=\"media\" data-alt=\"An arrow extends from 3 x in the first binomial to 2 x in the second binomial. A second arrow extends from 3 x in the first binomial to minus 5 in the second binomial. A third arrow extends from y in the first binomial to 2 x in the second binomial. A fourth arrow extends from y in the first binomial to minus 5 in the second binomial.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_018b_img_new.jpg\" alt=\"An arrow extends from 3 x in the first binomial to 2 x in the second binomial. A second arrow extends from 3 x in the first binomial to minus 5 in the second binomial. A third arrow extends from y in the first binomial to 2 x in the second binomial. A fourth arrow extends from y in the first binomial to minus 5 in the second binomial.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 44.0812%\">Multiply the <em data-effect=\"italics\">First<\/em>.<\/td>\r\n<td style=\"width: 55.8304%\">[latex]\\begin{array}{ccccccc} {\\color{red}{6x^2}} &amp; + &amp; \\rule{0.5cm}{0.4pt} &amp; + &amp; \\rule{0.5cm}{0.4pt} &amp;+&amp; \\rule{0.5cm}{0.4pt} \\\\ F&amp;&amp;O&amp;&amp;I&amp;&amp;L \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 44.0812%\">Multiply the <em data-effect=\"italics\">Outer<\/em>.<\/td>\r\n<td style=\"width: 55.8304%\">[latex]\\begin{array}{ccccccc} 6x^2 &amp; {\\color{red}{-}} &amp; {\\color{red}{15x}} &amp; + &amp; \\rule{0.5cm}{0.4pt} &amp;+&amp; \\rule{0.5cm}{0.4pt} \\\\ F&amp;&amp;O&amp;&amp;I&amp;&amp;L \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 44.0812%\">Multiply the <em data-effect=\"italics\">Inner<\/em>.<\/td>\r\n<td style=\"width: 55.8304%\">[latex]\\begin{array}{ccccccc} 6x^2 &amp; - &amp; 15x &amp; {\\color{red}{-}} &amp; {\\color{red}{2xy}} &amp;+&amp; \\rule{0.5cm}{0.4pt} \\\\ F&amp;&amp;O&amp;&amp;I&amp;&amp;L \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 44.0812%\">Multiply the <em data-effect=\"italics\">Last<\/em>.<\/td>\r\n<td style=\"width: 55.8304%\">[latex]\\begin{array}{ccccccc} 6x^2 &amp; - &amp; 15x &amp; - &amp; 2xy &amp; {\\color{red}{+}}&amp; {\\color{red}{5y}} \\\\ F&amp;&amp;O&amp;&amp;I&amp;&amp;L \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 44.0812%\">Combine like terms\u2014there are none.<\/td>\r\n<td style=\"width: 55.8304%\"><span id=\"eip-id1172187828927\" data-type=\"media\" data-alt=\"6 x squared minus 15 x minus 2 x y plus 5 y.\">[latex]6 x^2-15 x-2 x y+5 y[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596365886\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596365861\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596365863\" data-type=\"problem\">\r\n<p id=\"fs-id1169596365865\">Multiply: \\(\\left(10c-d\\right)\\left(c-6\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596555914\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596555916\">\\(10{c}^{2}-60c-cd+6d\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596557849\" data-type=\"problem\">\r\n<p id=\"fs-id1169596557851\">Multiply: \\(\\left(7x-y\\right)\\left(2x-5\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596439984\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596439987\">\\(14{x}^{2}-35x-2xy+5y\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169596396823\">Be careful of the exponents in the next example.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596452002\" data-type=\"problem\">\r\n<p id=\"fs-id1169596452004\">Multiply: \\(\\left({n}^{2}+4\\right)\\left(n-1\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"eip-id1172187963608\" class=\"unnumbered unstyled\" summary=\"This figure has three columns. At the top of the figure, the second column contains the product of two binomials, n squared plus 4 and n minus 1. One row down, the text in the first column says \u201cMultiply the first terms.\u201d The second column contains n cubed plus blank plus blank plus blank. Beneath n cubed is the letter F and beneath each blank are the letters O, I, and L, respectively. One row down, the text in the first column says \u201cMultiply the outer terms.\u201d The second column contains n cubed minus n squared plus blank plus blank. Below n cubed is F, below n squared is O, and below the blanks are I and L. One row down, the text in the first column says \u201cMultiply the inner terms.\u201d The second column contains n cubed minus n squared plus 4n plus blank. One row down, the text in the first column says \u201cMultiply the last terms.\u201d The second column contains the full expression, n cubed minus n squared plus 4n minus 4, with each letter of FOIL beneath each of the terms. At the bottom of the image, the text in the first column says \u201cCombine like terms\u2014there are none.\u201d In the right column is n cubed minus n squared plus 4n minus 4. In the third column is the product of the two binomials again, n squared plus 4 times n minus 1. An arrow extends from n cubed in the first binomial to n in the second binomial. A second arrow extends from n cubed in the first binomial to minus 1 in the second binomial. A third arrow extends from 4 in the first binomial to n in the second binomial. A fourth arrow extends from 4 in the first binomial to minus 1 in the second binomial.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>\\(\\left({n}^{2}+4\\right)\\left(n-1\\right)\\)<\/td>\r\n<td><span id=\"eip-id1172187963665\" data-type=\"media\" data-alt=\"The product of two binomials, n squared plus 4 and n minus 1. An arrow extends from n squared in the first binomial to n in the second binomial. A second arrow extends from n squared in the first binomial to minus 1 in the second binomial. A third arrow extends from 4 in the first binomial to n in the second binomial. A fourth arrow extends from 4 in the first binomial to minus 1 in the second binomial.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_019b_img_new.jpg\" alt=\"The product of two binomials, n squared plus 4 and n minus 1. An arrow extends from n squared in the first binomial to n in the second binomial. A second arrow extends from n squared in the first binomial to minus 1 in the second binomial. A third arrow extends from 4 in the first binomial to n in the second binomial. A fourth arrow extends from 4 in the first binomial to minus 1 in the second binomial.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the <em data-effect=\"italics\">First<\/em>.<\/td>\r\n<td>[latex]\\begin{array}{ccccccc} {\\color{red}{n^3}} &amp; + &amp; \\rule{0.5cm}{0.4pt} &amp; + &amp; \\rule{0.5cm}{0.4pt} &amp;+&amp; \\rule{0.5cm}{0.4pt} \\\\ F&amp;&amp;O&amp;&amp;I&amp;&amp;L \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the <em data-effect=\"italics\">Outer<\/em>.<\/td>\r\n<td>[latex]\\begin{array}{ccccccc} n^3 &amp; {\\color{red}{-}} &amp; {\\color{red}{n^2}} &amp; + &amp; \\rule{0.5cm}{0.4pt} &amp;+&amp; \\rule{0.5cm}{0.4pt} \\\\ F&amp;&amp;O&amp;&amp;I&amp;&amp;L \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the <em data-effect=\"italics\">Inner<\/em>.<\/td>\r\n<td>[latex]\\begin{array}{ccccccc} n^3 &amp; - &amp; n^2 &amp; + &amp; {\\color{red}{4n}} &amp;+&amp; \\rule{0.5cm}{0.4pt} \\\\ F&amp;&amp;O&amp;&amp;I&amp;&amp;L \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the <em data-effect=\"italics\">Last<\/em>.<\/td>\r\n<td>[latex]\\begin{array}{ccccccc} n^3 &amp; - &amp; n^2 &amp; + &amp; 4n &amp; {\\color{red}{-}}&amp; {\\color{red}{4}} \\\\ F&amp;&amp;O&amp;&amp;I&amp;&amp;L \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms\u2014there are none.<\/td>\r\n<td>[latex]n^3-n^2+4 n-4[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596258587\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596258591\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596258593\" data-type=\"problem\">\r\n<p id=\"fs-id1169596555098\">Multiply: \\(\\left({x}^{2}+6\\right)\\left(x-8\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596499635\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596499638\">\\({x}^{3}-8{x}^{2}+6x-48\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596557426\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596557429\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596557431\" data-type=\"problem\"><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596557431\" data-type=\"problem\">\r\n<p id=\"fs-id1169596557433\">Multiply: \\(\\left({y}^{2}+7\\right)\\left(y-9\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596499357\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596499359\">\\({y}^{3}-9{y}^{2}+7y-63\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596258587\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596258591\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596258593\" data-type=\"problem\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596371201\" data-type=\"problem\">\r\n<p id=\"fs-id1169596371203\">Multiply: \\(\\left(3pq+5\\right)\\left(6pq-11\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596366996\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1172187720059\" class=\"unnumbered unstyled\" style=\"height: 189px;width: 100%\" summary=\"This figure has three columns. At the top of the figure, the second column contains the product of two binomials, 3pq plus 5 and 6pq minus 11. One row down, the text in the first column says \u201cMultiply the first terms.\u201d The second column contains 18p squared q squared plus blank plus blank plus blank. Beneath 18p squared q squared is the letter F and beneath each blank are the letters O, I, and L, respectively. One row down, the text in the first column says \u201cMultiply the outer terms.\u201d The second column contains 18p squared q squared minus 33pq plus blank plus blank. Below 18p squared q squared is F, below 33pq is O, and below the blanks are I and L. One row down, the text in the first column says \u201cMultiply the inner terms.\u201d The second column contains 18p squared q squared minus 33pq plus 30pq plus blank. One row down, the text in the first column says \u201cMultiply the last terms.\u201d The second column contains the full expression, 18p squared q squared minus 33pq plus 30pq minus 55, with each letter of FOIL beneath each of the terms. At the bottom of the image, the text in the first column says \u201cCombine like terms.\u201d In the right column is 18p squared q squared minus 3pq minus 55. In the third column is the product of the two binomials again, 3pq plus 5 times 6pq minus 11. An arrow extends from 3pq in the first binomial to 6pq in the second binomial. A second arrow extends from 3pq in the first binomial to minus 11 in the second binomial. A third arrow extends from 5 in the first binomial to 6pq in the second binomial. A fourth arrow extends from 5 in the first binomial to minus 11 in the second binomial.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>[latex](3pq+5)(6pq-11)[\/latex]<\/td>\r\n<td><span id=\"eip-id1172187720114\" data-type=\"media\" data-alt=\"The product of two binomials, 3 p q plus 5 and 6 p q minus 11. An arrow extends from 3 p q in the first binomial to 6 p q in the second binomial. A second arrow extends from 3 p q in the first binomial to minus 11 in the second binomial. A third arrow extends from 5 in the first binomial to 6 p q in the second binomial. A fourth arrow extends from 5 in the first binomial to minus 11 in the second binomial.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_020b_img_new.jpg\" alt=\"The product of two binomials, 3 p q plus 5 and 6 p q minus 11. An arrow extends from 3 p q in the first binomial to 6 p q in the second binomial. A second arrow extends from 3 p q in the first binomial to minus 11 in the second binomial. A third arrow extends from 5 in the first binomial to 6 p q in the second binomial. A fourth arrow extends from 5 in the first binomial to minus 11 in the second binomial.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the <em data-effect=\"italics\">First<\/em>.<\/td>\r\n<td>\r\n<p style=\"text-align: left\">[latex] \\begin{array}{ccccccc} {\\color{red}{18p^2q^2}} &amp; + &amp; \\rule{.5cm}{0.4pt} &amp;\r\n+ &amp; \\rule{.5cm}{0.4pt} &amp; + &amp; \\rule{.5cm}{0.4pt} \\\\ F &amp; &amp; O &amp; &amp; I &amp; &amp; L \\\\ \\end{array} [\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the <em data-effect=\"italics\">Outer<\/em>.<\/td>\r\n<td>[latex]\\begin{array}{ccccccc} 18p^2q^2 &amp; {\\color{red}{-}} &amp;{\\color{red}{33pq}} &amp;\r\n+ &amp; \\rule{.5cm}{0.4pt} &amp; + &amp; \\rule{.5cm}{0.4pt} \\\\ F &amp; &amp; O &amp; &amp; I &amp; &amp; L \\\\ \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the <em data-effect=\"italics\">Inner<\/em>.<\/td>\r\n<td>[latex]\\begin{array}{ccccccc} 18p^2q^2 &amp; - &amp;33pq &amp;\r\n{\\color{red}{+}} &amp; {\\color{red}{30pq}} &amp; + &amp; \\rule{.5cm}{0.4pt} \\\\ F &amp; &amp; O &amp; &amp; I &amp; &amp; L \\\\ \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the <em data-effect=\"italics\">Last<\/em>.<\/td>\r\n<td>[latex]\\begin{array}{ccccccc} 18p^2q^2 &amp; - &amp;33pq &amp;\r\n+ &amp; 30pq &amp; {\\color{red}{-}}&amp; {\\color{red}{55}} \\\\ F &amp; &amp; O &amp; &amp; I &amp; &amp; L \\\\ \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>[latex]18 p^2 q^2-3 p q-55[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596557426\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596557429\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596499357\" data-type=\"solution\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 16.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596555522\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596555526\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596555528\" data-type=\"problem\">\r\n<p id=\"fs-id1169596555530\">Multiply: \\(\\left(2ab+5\\right)\\left(4ab-4\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596557487\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596384829\">\\(8{a}^{2}{b}^{2}+12ab-20\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596384862\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596384865\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596556552\" data-type=\"problem\"><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596556552\" data-type=\"problem\">\r\n<p id=\"fs-id1169596556554\">Multiply: \\(\\left(2xy+3\\right)\\left(4xy-5\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596296045\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596296047\">\\(8{x}^{2}{y}^{2}+2xy-15\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1 data-type=\"title\">Multiply a Binomial by a Binomial Using the Vertical Method<\/h1>\r\n<p id=\"fs-id1169596303991\">The FOIL method is usually the quickest method for multiplying two binomials, but it <em data-effect=\"italics\">only<\/em> works for binomials. You can use the Distributive Property to find the product of any two polynomials. Another method that works for all polynomials is the Vertical Method. It is very much like the method you use to multiply whole numbers. Look carefully at this example of multiplying two-digit numbers.<\/p>\r\n<span id=\"fs-id1169596304009\" data-type=\"media\" data-alt=\"This figure shows the vertical multiplication of 23 and 46. The number 23 is above the number 46. Below this, there is the partial product 138 over the partial product 92. The final product is at the bottom and is 1058. Text on the right side of the image says \u201cStart by multiplying 23 by 6 to get 138. Next, multiply 23 by 4, lining up the partial product in the correct columns. Last you add the partial products.\u201d\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_021_img_new.jpg\" alt=\"This figure shows the vertical multiplication of 23 and 46. The number 23 is above the number 46. Below this, there is the partial product 138 over the partial product 92. The final product is at the bottom and is 1058. Text on the right side of the image says \u201cStart by multiplying 23 by 6 to get 138. Next, multiply 23 by 4, lining up the partial product in the correct columns. Last you add the partial products.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1169596304017\">Now we\u2019ll apply this same method to multiply two binomials.<\/p>\r\n\r\n<div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 17<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div class=\"textbox__content\">\r\n\r\nMultiply using the Vertical Method: \\(\\left(3y-1\\right)\\left(2y-6\\right)\\).\r\n\r\n<strong>Solution<\/strong>\r\n\r\nIt does not matter which binomial goes on the top.\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 30.6922%\">Setup for Vertical multiplication<\/td>\r\n<td style=\"text-align: right;width: 35.7013%\">[latex]\\begin{array}{r} 3y-1 \\\\ \\times \\quad {\\color{blue}{ 2y}}- {\\color{red}{6}} \\\\ \\hline \\end{array}[\/latex]<\/td>\r\n<td style=\"width: 33.5155%\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 30.6922%\">Multiply \\(3y-1\\) by [latex]\\color{red} -6[\/latex]\r\nMultiple \\(3y-1\\) by [latex]\\color{blue} 2y[\/latex]<\/td>\r\n<td style=\"text-align: right;width: 35.7013%\">[latex]\\begin{array}{r} {\\color{red}{-18y+6}} \\\\ {\\color{blue}{6{y}^{2} -2y}} \\hspace{0.9cm} \\\\ \\hline \\end{array}[\/latex]<\/td>\r\n<td style=\"width: 33.5155%\">Partial Product \\(-18y+6\\)\r\nPartial Product \\(6{y}^{2} -2y\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 30.6922%\">Add like terms.<\/td>\r\n<td style=\"text-align: right;width: 35.7013%\">[latex]6y^2 \\hspace{0.2cm} -20 y \\hspace{0.2cm} +6[\/latex]<\/td>\r\n<td style=\"width: 33.5155%\">Product \\(6{y}^{2} - 20y+6\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nIf you use the FOIL method to multiply these binomials you will notice that the partial products are the same as the terms in the FOIL method.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 17.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1169596556869\">Multiply using the Vertical Method: \\(\\left(5m-7\\right)\\left(3m-6\\right)\\).<\/p>\r\n\r\n<details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596556869\">\\(15{m}^{2}-51m+42\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 17.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596556861\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596556861\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596556864\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596556864\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596497567\" data-type=\"solution\">\r\n<div id=\"fs-id1169596497567\" data-type=\"solution\">\r\n<p id=\"fs-id1169596497570\">Multiply using the Vertical Method: \\(\\left(6b-5\\right)\\left(7b-3\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596497595\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596497595\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596497599\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596497599\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596497601\" data-type=\"problem\">\r\n<div id=\"fs-id1169596497601\" data-type=\"problem\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596499276\">\\(42{b}^{2}-53b+15\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169596499713\">We have now used three methods for multiplying binomials. Be sure to practice each method, and try to decide which one you prefer. The methods are listed here all together, to help you remember them.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Multiplying Two Binomials<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nTo multiply binomials, use the:\r\n<ul>\r\n \t<li style=\"list-style-type: none\">\r\n<ul id=\"fs-id1169596499726\" data-bullet-style=\"bullet\">\r\n \t<li>Distributive Property<\/li>\r\n \t<li>FOIL Method<\/li>\r\n \t<li>Vertical Method<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596499718\" data-type=\"note\">\r\n<div id=\"fs-id1169596499718\" data-type=\"note\">\r\n<p id=\"fs-id1171792350534\">Remember, FOIL only works when multiplying two binomials.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<h1 data-type=\"title\">Multiply a Trinomial by a Binomial<\/h1>\r\n<p id=\"fs-id1169596410089\">We have multiplied monomials by monomials, monomials by polynomials, and binomials by binomials. Now we\u2019re ready to multiply a <span class=\"no-emphasis\" data-type=\"term\">trinomial<\/span> by a <span class=\"no-emphasis\" data-type=\"term\">binomial<\/span>. Remember, FOIL will not work in this case, but we can use either the Distributive Property or the Vertical Method. We first look at an example using the Distributive Property.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 18<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596410109\" data-type=\"problem\">\r\n<p id=\"fs-id1169596410111\">Multiply using the Distributive Property: \\(\\left(b+3\\right)\\left(2{b}^{2}-5b+8\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596558245\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1172187617554\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the first row, the right column contains the product of a binomial, b plus 3, and a trinomial, 2b squared minus 5b plus 8. Two red arrows extend from the trinomial, terminating at b and 3 in the binomial. In the second row, the text in the left column says \u201cDistribute.\u201d In the right column is b times 2b squared minus 5b plus 8 plus 3 times 2b squared minus 5b plus 8, where 2b squared minus 5b plus 8 is in parentheses twice. In the third row, the text in the left column says \u201cMultiply.\u201d In the right column is 2b cubed minus 5b squared plus 8b plus 6b squared minus 15b plus 24. In the last row, the text in the left column says \u201cCombine like terms.\u201d In the right column is 2b cubed plus b squared minus 7b plus 24.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1172187617574\" data-type=\"media\" data-alt=\"The product of a binomial, b plus 3, and a trinomial, 2 b squared minus 5 b plus 8. Two arrows extend from the trinomial, terminating at b and 3 in the binomial.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_024a_img_new.jpg\" alt=\"The product of a binomial, b plus 3, and a trinomial, 2 b squared minus 5 b plus 8. Two arrows extend from the trinomial, terminating at b and 3 in the binomial.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td><span id=\"eip-id1172187617591\" data-type=\"media\" data-alt=\"The sum of two products, the product of b and 2 b squared minus 5 b plus 8, and the product of 3 and 2 b squared minus 5 b plus 8.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_024b_img_new.jpg\" alt=\"The sum of two products, the product of b and 2 b squared minus 5 b plus 8, and the product of 3 and 2 b squared minus 5 b plus 8.\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]2 b^3-5b^2+8b+6b^2-15 b+24[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td><span id=\"eip-id1172187617625\" data-type=\"media\" data-alt=\"2 b cubed plus b squared minus 7 b plus 24.\">[latex]2 b^3+b^2-7 b+24[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 18.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596369771\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596369775\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596369777\" data-type=\"problem\">\r\n<p id=\"fs-id1169596369779\">Multiply using the Distributive Property: \\(\\left(y-3\\right)\\left({y}^{2}-5y+2\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<details open=\"open\"><summary>Show answer<\/summary>\r\n<div data-type=\"solution\">\r\n\r\n\\({y}^{3}-8{y}^{2}+17y-6\\)\r\n\r\n<\/div>\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 18.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596348894\" data-type=\"problem\">\r\n<p id=\"fs-id1169596348896\">Multiply using the Distributive Property: \\(\\left(x+4\\right)\\left(2{x}^{2}-3x+5\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596555021\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596555023\">\\(2{x}^{3}+5{x}^{2}-7x+20\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169596498300\">Now let\u2019s do this same multiplication using the Vertical Method.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 19<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596498309\" data-type=\"problem\">\r\n<p id=\"fs-id1169596498311\">Multiply using the Vertical Method: \\(\\left(b+3\\right)\\left(2{b}^{2}-5b+8\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596554965\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1169596554970\">It is easier to put the polynomial with fewer terms on the bottom because we get fewer partial products this way.<\/p>\r\n\r\n<table id=\"eip-id1172187963535\" class=\"unnumbered unstyled\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the right column contains the vertical multiplication of 2b squared minus 5b plus 8 and b plus 3. The text in the left column says \u201cMultiply 2b squared minus 5b plus 8 by 3.\u201d In the right column is the partial product 6b squared minus 15b plus 24. One line down, the text in the left column says \u201cMultiply 2b squared minus 5b plus 8 by b.\u201d In the right column is the partial product 2b cubed minus 5b squared plus 8b. One line down, the text in the left column says \u201cAdd like terms.\u201d In the right column is the fully expanded expression: 2b cubed plus b squared minus 7b plus 24.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td data-valign=\"bottom\">Rewrite the question in vertical setup<\/td>\r\n<td style=\"text-align: right\">[latex]\\begin{array}{r} 2 b^2-5 b+8 \\\\ \\times \\quad {\\color{blue}{ b}}+ {\\color{red}{3}} \\\\ \\hline \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply (2<em data-effect=\"italics\">b<\/em><sup>2<\/sup> \u2212 5<em data-effect=\"italics\">b<\/em> + 8) by [latex]\\color{red}3[\/latex].\r\nMultiply (2<em data-effect=\"italics\">b<\/em><sup>2<\/sup> \u2212 5<em data-effect=\"italics\">b<\/em> + 8) by [latex]\\color{blue}b[\/latex].<\/td>\r\n<td style=\"text-align: right\">[latex]\\begin{array}{r} {\\color{red}{6 b^2-15 b+24}} \\\\ {\\color{blue}{2b^3-5b^2+8b}} \\hspace{0.9cm} \\\\ \\hline \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add like terms.<\/td>\r\n<td style=\"text-align: right\">[latex]2 b^3\u00a0 +b^2 \\hspace{0.2cm} -7 b \\hspace{0.2cm} +24[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>There are no more like terms that can be collected.<\/td>\r\n<td>[latex]2 b^3+b^2-7 b+24[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 19.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596382893\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596382897\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596382899\" data-type=\"problem\">\r\n<p id=\"fs-id1169596382901\">Multiply using the Vertical Method: \\(\\left(y-3\\right)\\left({y}^{2}-5y+2\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596555484\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596555486\">\\({y}^{3}-8{y}^{2}+17y-6\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 19.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596557069\" data-type=\"problem\">\r\n<p id=\"fs-id1169596557071\">Multiply using the Vertical Method: \\(\\left(x+4\\right)\\left(2{x}^{2}-3x+5\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596559250\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596559252\">\\(2{x}^{3}+5{x}^{2}-7x+20\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169596559287\">We have now seen two methods you can use to multiply a <span class=\"no-emphasis\" data-type=\"term\">trinomial<\/span> by a binomial. After you practice each method, you\u2019ll probably find you prefer one way over the other. We list both methods are listed here, for easy reference.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Multiply a Trinomial by a Binomial<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1169596559298\">To multiply a trinomial by a binomial, use the:<\/p>\r\n\r\n<ul id=\"fs-id1169596291508\" data-bullet-style=\"bullet\">\r\n \t<li>Distributive Property<\/li>\r\n \t<li>Vertical Method<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596559293\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n\r\nAccess these online resources for additional instruction and practice with multiplying polynomials:\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596291522\" class=\"media-2\" data-type=\"note\">\r\n<ul id=\"fs-id1169596291531\" data-display=\"block\">\r\n \t<li><a href=\"https:\/\/openstax.org\/l\/25MultiplyExp1\">Multiplying Exponents 1<\/a><\/li>\r\n \t<li><a href=\"https:\/\/openstax.org\/l\/25MultiplyExp2\">Multiplying Exponents 2<\/a><\/li>\r\n \t<li><a href=\"https:\/\/openstax.org\/l\/25MultiplyExp3\">Multiplying Exponents 3<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1 data-type=\"title\">Key Concepts<\/h1>\r\n<ul id=\"fs-id1169596457026\" data-bullet-style=\"bullet\">\r\n \t<li><strong data-effect=\"bold\">FOIL Method for Multiplying Two Binomials<\/strong>\u2014To multiply two binomials:\r\n<ol id=\"fs-id1168741741690\" class=\"stepwise\" type=\"1\">\r\n \t<li>Multiply the <strong data-effect=\"bold\">First<\/strong> terms.<\/li>\r\n \t<li>Multiply the <strong data-effect=\"bold\">Outer<\/strong> terms.<\/li>\r\n \t<li>Multiply the <strong data-effect=\"bold\">Inner<\/strong> terms.<\/li>\r\n \t<li>Multiply the <strong data-effect=\"bold\">Last<\/strong> terms.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Multiplying Two Binomials<\/strong>\u2014To multiply binomials, use the:\r\n<ul id=\"fs-id1169596557780\" data-bullet-style=\"open-circle\">\r\n \t<li>Distributive Property (<a class=\"autogenerated-content\" href=\"#fs-id1169596308817\">(Figure)<\/a>)<\/li>\r\n \t<li>FOIL Method (<a class=\"autogenerated-content\" href=\"#fs-id1169596450766\">(Figure)<\/a>)<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Multiplying a Trinomial by a Binomial<\/strong>\u2014To multiply a trinomial by a binomial, use the:\r\n<ul id=\"fs-id1169596557816\" data-bullet-style=\"open-circle\">\r\n \t<li>Distributive Property (<a class=\"autogenerated-content\" href=\"#fs-id1169596410105\">(Figure)<\/a>)<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h1 style=\"text-align: left\" data-type=\"title\">Practice Makes Perfect<\/h1>\r\n<h2 style=\"text-align: left\" data-type=\"title\">Multiply a Polynomial by a Monomial<\/h2>\r\n<p id=\"fs-id1168745407238\">In the following exercises, multiply.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%;height: 476px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">1. \\(4\\left(w+10\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">2. \\(6\\left(b+8\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">3. \\(-3\\left(a+7\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">4. \\(-5\\left(p+9\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">5. \\(2\\left(x-7\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">6. \\(7\\left(y-4\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">7. \\(-3\\left(k-4\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">8. \\(-8\\left(j-5\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">9. \\(q\\left(q+5\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">10. \\(k\\left(k+7\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">11. \\(-b\\left(b+9\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">12. \\(-y\\left(y+3\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">13. \\(-x\\left(x-10\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">14. \\(-p\\left(p-15\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">15. \\(6r\\left(4r+s\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">16. \\(5c\\left(9c+d\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">17. \\(12x\\left(x-10\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">18. \\(9m\\left(m-11\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">19. \\(-9a\\left(3a+5\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">20. \\(-4p\\left(2p+7\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">21. \\(3\\left({p}^{2}+10p+25\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">22. \\(6\\left({y}^{2}+8y+16\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">23. \\(-8x\\left({x}^{2}+2x-15\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">24. \\(-5t\\left({t}^{2}+3t-18\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">25. \\(5{q}^{3}\\left({q}^{3}-2q+6\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">26. \\(4{x}^{3}\\left({x}^{4}-3x+7\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">27. \\(-8y\\left({y}^{2}+2y-15\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">28. \\(-5m\\left({m}^{2}+3m-18\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">29. \\(5{q}^{3}\\left({q}^{2}-2q+6\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">30. \\(9{r}^{3}\\left({r}^{2}-3r+5\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">31. \\(-4{z}^{2}\\left(3{z}^{2}+12z-1\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">32. \\(-3{x}^{2}\\left(7{x}^{2}+10x-1\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">33. \\(\\left(2m-9\\right)m\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">34. \\(\\left(8j-1\\right)j\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">35. \\(\\left(w-6\\right)\\cdot 8\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">36. \\(\\left(k-4\\right)\\cdot 5\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">37. \\(4\\left(x+10\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">38. \\(6\\left(y+8\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">39. \\(15\\left(r-24\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">40. \\(12\\left(v-30\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">41. \\(-3\\left(m+11\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">42. \\(-4\\left(p+15\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">43. \\(-8\\left(z-5\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">44. \\(-3\\left(x-9\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">45. \\(u\\left(u+5\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">46. \\(q\\left(q+7\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">47. \\(n\\left({n}^{2}-3n\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">48. \\(s\\left({s}^{2}-6s\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">49. \\(6x\\left(4x+y\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">50. \\(5a\\left(9a+b\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">51. \\(5p\\left(11p-5q\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">52. \\(12u\\left(3u-4v\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">53. \\(3\\left({v}^{2}+10v+25\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">54. \\(6\\left({x}^{2}+8x+16\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">55. \\(2n\\left(4{n}^{2}-4n+1\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">56. \\(3r\\left(2{r}^{2}-6r+2\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">57. \\(-8y\\left({y}^{2}+2y-15\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">58. \\(5m\\left({m}^{2}+3m+8\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">59. \\(5{q}^{3}\\left({q}^{2}-2q+6\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">60. \\(9{r}^{3}\\left({r}^{2}-3r+5\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">61. \\(-4{z}^{2}\\left(3{z}^{2}+12z-1\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">62. \\(-3{x}^{2}\\left(7{x}^{2}+10x-1\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">63. \\(\\left(2y-9\\right)y\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">64. \\(\\left(8b-1\\right)b\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2 id=\"fs-id1169596387411\">Multiply a Binomial by a Binomial<\/h2>\r\n<p id=\"fs-id1168745394224\">In the following exercises, multiply the following binomials using: a) the Distributive Property b) the FOIL method c) the Vertical Method.<\/p>\r\n\r\n<div id=\"fs-id1169596387420\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596387422\" data-type=\"problem\">\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">65. \\(\\left(w+5\\right)\\left(w+7\\right)\\)<\/td>\r\n<td style=\"width: 50%\">66. \\(\\left(y+9\\right)\\left(y+3\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">67. \\(\\left(p+11\\right)\\left(p-4\\right)\\)<\/td>\r\n<td style=\"width: 50%\">68. \\(\\left(q+4\\right)\\left(q-8\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1169596387424\">In the following exercises, multiply the binomials. Use any method.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<table style=\"border-collapse: collapse;width: 100%;height: 140px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">69. \\(\\left(x+8\\right)\\left(x+3\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">70. \\(\\left(y+7\\right)\\left(y+4\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">71. \\(\\left(y-6\\right)\\left(y-2\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">72. \\(\\left(x-7\\right)\\left(x-2\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">73. \\(\\left(w-4\\right)\\left(w+7\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">74. \\(\\left(q-5\\right)\\left(q+8\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">75. \\(\\left(p+12\\right)\\left(p-5\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">76. \\(\\left(m+11\\right)\\left(m-4\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">77. \\(\\left(6p+5\\right)\\left(p+1\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">78. \\(\\left(7m+1\\right)\\left(m+3\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">79. \\(\\left(2t-9\\right)\\left(10t+1\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">80. \\(\\left(3r-8\\right)\\left(11r+1\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">81. \\(\\left(5x-y\\right)\\left(3x-6\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">82. \\(\\left(10a-b\\right)\\left(3a-4\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">83. \\(\\left(a+b\\right)\\left(2a+3b\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">84. \\(\\left(r+s\\right)\\left(3r+2s\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">85. \\(\\left(4z-y\\right)\\left(z-6\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">86. \\(\\left(5x-y\\right)\\left(x-4\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">87. \\(\\left({x}^{2}+3\\right)\\left(x+2\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">88. \\(\\left({y}^{2}-4\\right)\\left(y+3\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">89. \\(\\left({x}^{2}+8\\right)\\left({x}^{2}-5\\right)\\)<\/td>\r\n<td style=\"width: 50%\">90. \\(\\left({y}^{2}-7\\right)\\left({y}^{2}-4\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">91. \\(\\left(5ab-1\\right)\\left(2ab+3\\right)\\)<\/td>\r\n<td style=\"width: 50%\">92. \\(\\left(2xy+3\\right)\\left(3xy+2\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">93. \\(\\left(6pq-3\\right)\\left(4pq-5\\right)\\)<\/td>\r\n<td style=\"width: 50%\">94. \\(\\left(3rs-7\\right)\\left(3rs-4\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2 id=\"fs-id1169596402196\"><strong data-effect=\"bold\">\r\n<\/strong>Multiply a Trinomial by a Binomial<\/h2>\r\n<p id=\"fs-id1168742142113\">In the following exercises, multiply using a) the Distributive Property b) the Vertical Method.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">95. \\(\\left(x+5\\right)\\left({x}^{2}+4x+3\\right)\\)<\/td>\r\n<td style=\"width: 50%\">96. \\(\\left(u+4\\right)\\left({u}^{2}+3u+2\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">97. \\(\\left(y+8\\right)\\left(4{y}^{2}+y-7\\right)\\)<\/td>\r\n<td style=\"width: 50%\">98. \\(\\left(a+10\\right)\\left(3{a}^{2}+a-5\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div id=\"fs-id1169596556594\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596556596\" data-type=\"problem\">\r\n<p id=\"fs-id1169596556598\">In the following exercises, multiply. Use either method.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">99. \\(\\left(w-7\\right)\\left({w}^{2}-9w+10\\right)\\)<\/td>\r\n<td style=\"width: 50%\">100. \\(\\left(p-4\\right)\\left({p}^{2}-6p+9\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">101. \\(\\left(3q+1\\right)\\left({q}^{2}-4q-5\\right)\\)<\/td>\r\n<td style=\"width: 50%\">102. \\(\\left(6r+1\\right)\\left({r}^{2}-7r-9\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div id=\"fs-id1169596556256\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596556258\" data-type=\"problem\">\r\n<h2 id=\"fs-id1169596556260\">Mixed Practice<\/h2>\r\n<\/div>\r\n<\/div>\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">103. \\(\\left(10y-6\\right)+\\left(4y-7\\right)\\)<\/td>\r\n<td style=\"width: 50%\">104. \\(\\left(15p-4\\right)+\\left(3p-5\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">105. \\(\\left({x}^{2}-4x-34\\right)-\\left({x}^{2}+7x-6\\right)\\)<\/td>\r\n<td style=\"width: 50%\">106. \\(\\left({j}^{2}-8j-27\\right)-\\left({j}^{2}+2j-12\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">107. \\(5q\\left(3{q}^{2}-6q+11\\right)\\)<\/td>\r\n<td style=\"width: 50%\">108. \\(8t\\left(2{t}^{2}-5t+6\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">109. \\(\\left(s-7\\right)\\left(s+9\\right)\\)<\/td>\r\n<td style=\"width: 50%\">110. \\(\\left(x-5\\right)\\left(x+13\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">111. \\(\\left({y}^{2}-2y\\right)\\left(y+1\\right)\\)<\/td>\r\n<td style=\"width: 50%\">112. \\(\\left({a}^{2}-3a\\right)\\left(4a+5\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">113. \\(\\left(3n-4\\right)\\left({n}^{2}+n-7\\right)\\)<\/td>\r\n<td style=\"width: 50%\">114. \\(\\left(6k-1\\right)\\left({k}^{2}+2k-4\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">115. \\(\\left(7p+10\\right)\\left(7p-10\\right)\\)<\/td>\r\n<td style=\"width: 50%\">116. \\(\\left(3y+8\\right)\\left(3y-8\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">117. \\(\\left(4{m}^{2}-3m-7\\right){m}^{2}\\)<\/td>\r\n<td style=\"width: 50%\">118. \\(\\left(15{c}^{2}-4c+5\\right){c}^{4}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">119. \\(\\left(5a+7b\\right)\\left(5a+7b\\right)\\)<\/td>\r\n<td style=\"width: 50%\">120. \\(\\left(3x-11y\\right)\\left(3x-11y\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">121. \\(\\left(4y+12z\\right)\\left(4y-12z\\right)\\)<\/td>\r\n<td style=\"width: 50%\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2 style=\"text-align: left\" data-type=\"title\">Everyday Math<\/h2>\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1169596398985\">122.<strong> Mental math<\/strong> You can use binomial multiplication to multiply numbers without a calculator. Say you need to multiply 13 times 15. Think of 13 as \\(10+3\\) and 15 as \\(10+5\\).<\/p>\r\n\r\n<ol id=\"fs-id1168742188094\" class=\"circled\" type=\"a\">\r\n \t<li>Multiply \\(\\left(10+3\\right)\\left(10+5\\right)\\) by the FOIL method.<\/li>\r\n \t<li>Multiply \\(13\\cdot 15\\) without using a calculator.<\/li>\r\n \t<li>Which way is easier for you? Why?<\/li>\r\n<\/ol>\r\n<\/td>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1169596498098\">123.<strong data-effect=\"bold\"> Mental math<\/strong> You can use binomial multiplication to multiply numbers without a calculator. Say you need to multiply 18 times 17. Think of 18 as \\(20-2\\) and 17 as \\(20-3\\).<\/p>\r\n\r\n<ol id=\"fs-id1168742196535\" class=\"circled\" type=\"a\">\r\n \t<li>Multiply \\(\\left(20-2\\right)\\left(20-3\\right)\\) by the FOIL method.<\/li>\r\n \t<li>Multiply \\(18\\cdot 17\\) without using a calculator.<\/li>\r\n \t<li>Which way is easier for you? Why?<\/li>\r\n<\/ol>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2 style=\"text-align: left\" data-type=\"title\">Writing Exercises<\/h2>\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">124. Which method do you prefer to use when multiplying two binomials: the Distributive Property, the FOIL method, or the Vertical Method? Why?<\/td>\r\n<td style=\"width: 50%\">125. Which method do you prefer to use when multiplying a trinomial by a binomial: the Distributive Property or the Vertical Method? Why?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1169596554478\">126. Multiply the following:<\/p>\r\n<p id=\"fs-id1169596554482\">\\(\\begin{array}{c}\\left(x+2\\right)\\left(x-2\\right)\\hfill \\\\ \\left(y+7\\right)\\left(y-7\\right)\\hfill \\\\ \\left(w+5\\right)\\left(w-5\\right)\\hfill \\end{array}\\)<\/p>\r\n<p id=\"fs-id1169596411012\">Explain the pattern that you see in your answers.<\/p>\r\n<\/td>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1169596411028\">127. Multiply the following:<\/p>\r\n<p id=\"fs-id1169596411031\">\\(\\begin{array}{c}\\left(m-3\\right)\\left(m+3\\right)\\hfill \\\\ \\left(n-10\\right)\\left(n+10\\right)\\hfill \\\\ \\left(p-8\\right)\\left(p+8\\right)\\hfill \\end{array}\\)<\/p>\r\n<p id=\"fs-id1169596387870\">Explain the pattern that you see in your answers.<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1169596387886\">128. Multiply the following:<\/p>\r\n<p id=\"fs-id1169596387889\">\\(\\begin{array}{c}\\left(p+3\\right)\\left(p+3\\right)\\hfill \\\\ \\left(q+6\\right)\\left(q+6\\right)\\hfill \\\\ \\left(r+1\\right)\\left(r+1\\right)\\hfill \\end{array}\\)<\/p>\r\n<p id=\"fs-id1169596387994\">Explain the pattern that you see in your answers.<\/p>\r\n<\/td>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1169596556729\">129. Multiply the following:<\/p>\r\n<p id=\"fs-id1169596556732\">\\(\\begin{array}{c}\\left(x-4\\right)\\left(x-4\\right)\\hfill \\\\ \\left(y-1\\right)\\left(y-1\\right)\\hfill \\\\ \\left(z-7\\right)\\left(z-7\\right)\\hfill \\end{array}\\)<\/p>\r\n<p id=\"fs-id1169596556837\">Explain the pattern that you see in your answers.<\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h1 style=\"text-align: left\">Answers<\/h1>\r\n<table style=\"border-collapse: collapse;width: 100%;height: 320px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">1. \\(4w+40\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">3. \\(-3a-21\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">5. \\(2x-14\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">7. \\(-3k+12\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">9. \\({q}^{2}+5q\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">11. \\(\\text{-}{b}^{2}-9b\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">13. \\(\\text{-}{x}^{2}+10x\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">15. \\(24{r}^{2}+6rs\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">17. \\(12{x}^{2}-120x\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">19. \\(-27{a}^{2}-45a\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">21. \\(3{p}^{2}+30p+75\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">23. \\(-8{x}^{3}-16{x}^{2}+120x\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">25. \\(5{q}^{6}-10{q}^{4}+30{q}^{3}\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">27. \\(-8{y}^{3}-16{y}^{2}+120y\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">29. \\(5{q}^{5}-10{q}^{4}+30{q}^{3}\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">31. \\(-12{z}^{4}-48{z}^{3}+4{z}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">33. \\(2{m}^{2}-9m\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">35. \\(8w-48\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">37. \\(4x+40\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">39. \\(15r-360\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">41. \\(-3m-33\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">43. \\(-8z+40\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">45. \\({u}^{2}+5u\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">47. \\({n}^{3}-3{n}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">49. \\(24{x}^{2}+6xy\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">51. \\(55{p}^{2}-25pq\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">53. \\(3{v}^{2}+30v+75\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">55. \\(8{n}^{3}-8{n}^{2}+2n\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">57. \\(-8{y}^{3}-16{y}^{2}+120y\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">59. \\(5{q}^{5}-10{q}^{4}+30{q}^{3}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">61. \\(-12{z}^{4}-48{z}^{3}+4{z}^{2}\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">63. \\(2{y}^{2}-9y\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">65. \\({w}^{2}+12w+35\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">67. \\({p}^{2}+7p-44\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">69. \\({x}^{2}+11x+24\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">71. \\({y}^{2}-8y+12\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">73. \\({w}^{2}+3w-28\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">75. \\({p}^{2}+7p-60\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">77. \\(6{p}^{2}+11p+5\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">79. \\(20{t}^{2}-88t-9\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">81. \\(15{x}^{2}-3xy-30x+6y\\)<\/td>\r\n<td style=\"width: 50%\">83. \\(2{a}^{2}+5ab+3{b}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">85. \\(4{z}^{2}-24z-zy+6y\\)<\/td>\r\n<td style=\"width: 50%\">87. \\({x}^{3}+2{x}^{2}+3x+6\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">89. \\({x}^{4}+3{x}^{2}-40\\)<\/td>\r\n<td style=\"width: 50%\">91. \\(10{a}^{2}{b}^{2}+13ab-3\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">93. \\(24{p}^{2}{q}^{2}-42pq+15\\)<\/td>\r\n<td style=\"width: 50%\">95. \\({x}^{3}+9{x}^{2}+23x+15\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">97. \\(4{y}^{3}+33{y}^{2}+y-56\\)<\/td>\r\n<td style=\"width: 50%\">99. \\({w}^{3}-16{w}^{2}+73w-70\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">101. \\(3{q}^{3}-11{q}^{2}-19q-5\\)<\/td>\r\n<td style=\"width: 50%\">103. \\(14y-13\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">105. \\(-11x-28\\)<\/td>\r\n<td style=\"width: 50%\">107. \\(15{q}^{3}-30{q}^{2}+55q\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">109. \\({s}^{2}+2s-63\\)<\/td>\r\n<td style=\"width: 50%\">111. \\({y}^{3}-{y}^{2}-2y\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">113. \\(3{n}^{3}-{n}^{2}-25n+28\\)<\/td>\r\n<td style=\"width: 50%\">115. \\(49{p}^{2}-100\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">117. \\(4{m}^{4}-3{m}^{3}-7{m}^{2}\\)<\/td>\r\n<td style=\"width: 50%\">119. \\(25{a}^{2}+70ab+49{b}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">121. \\(16{y}^{2}-144{z}^{2}\\)<\/td>\r\n<td style=\"width: 50%\">123. a) 306 b) 306 c) Answers will vary.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">125. Answers will vary.<\/td>\r\n<td style=\"width: 50%\">127.\r\n\\({m}^2-9\\)\r\n\\({n}^2-100\\)\r\n\\({p}^2-64\\)\r\nAnswers will vary.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">129.\r\n\\({x}^2-8x+16\\)\r\n\\({y}^2-2y+1\\)\r\n\\({z}^2-14z+49\\)\r\nAnswers will vary.<\/td>\r\n<td style=\"width: 50%\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h1>Attributions<\/h1>\r\nThis chapter has been adapted from \u201cMultiply Polynomials\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.\r\n\r\n<!-- pb_fixme -->","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Multiply a polynomial by a monomial<\/li>\n<li>Multiply a binomial by a binomial<\/li>\n<li>Multiply a trinomial by a binomial<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Multiply a Polynomial by a Monomial<\/h1>\n<p id=\"fs-id1169596306663\">We have used the Distributive Property to simplify expressions like <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d71f69340ad1256ed810b93d107ac6ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\" \/>. You multiplied both terms in the parentheses, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bb53ce30a3ff5b6ca87fc6e1eb6588a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4cf5983200020861d6bb094a2f1bf0ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>, by 2, to get <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-73876cda295a59bd0fa7aefb814e18b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"50\" style=\"vertical-align: 0px;\" \/>. With this chapter\u2019s new vocabulary, you can say you were multiplying a binomial, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a8795f7a8007f8fdd0059e384627e4fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\" \/>, by a monomial, 2<\/p>\n<p id=\"fs-id1169596291896\">Multiplying a <span class=\"no-emphasis\" data-type=\"term\">binomial<\/span> by a <span class=\"no-emphasis\" data-type=\"term\">monomial<\/span> is nothing new for you! Here\u2019s an example:<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596219597\" data-type=\"problem\">\n<p id=\"fs-id1169596367284\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9b8f006629982556e8d26b5fe5fa7dd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596396832\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172187674776\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the first row, the right column contains the expression 4 times x plus 3, with x plus 3 in parentheses. Two red arrows extend from 4, terminating at x and 3. In the second row, the text in the left column says \u201cDistribute.\u201d In the right column is 4 times x plus 4 times 3. In the last row, the text in the left column says \u201cSimplify.\u201d In the right column is 4x plus 12.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172188943362\" data-type=\"media\" data-alt=\"4 times x plus 3. Two arrows extend from 4, terminating at x and 3.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/CNX_ElemAlg_Figure_06_03_001a_img_new.jpg\" alt=\"4 times x plus 3. Two arrows extend from 4, terminating at x and 3.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1172189039404\" data-type=\"media\" data-alt=\"4 times x plus 4 times 3.\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e913509edab85b7499069c3c68173c21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#92;&#99;&#100;&#111;&#116;&#125;&#32;&#120;&#32;&#43;&#32;&#52;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#92;&#99;&#100;&#111;&#116;&#125;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"68\" style=\"vertical-align: -2px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bb9256048113e82068d0b82bbd9027cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"58\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596362495\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596235948\" data-type=\"exercise\">\n<div id=\"fs-id1169596309264\" data-type=\"problem\">\n<p id=\"fs-id1169596274677\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6636c1903d074b62f5b42319558cc572_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596261412\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596295063\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ae9ecb00ccd1188839d7d71430d74e21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#43;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"58\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596360411\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596303507\" data-type=\"exercise\">\n<div id=\"fs-id1169596238777\" data-type=\"problem\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596238777\" data-type=\"problem\">\n<p id=\"fs-id1169596317308\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d1069275c0a6cfa16881a9816c4b487d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#49;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596279454\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596319249\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-26f40472ce3d68874d71098b4f938c32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#121;&#43;&#51;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"58\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596360411\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596303507\" data-type=\"exercise\">\n<div id=\"fs-id1169596279454\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596314988\" data-type=\"problem\">\n<p id=\"fs-id1169596309898\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a2e0c915563e8d80061620b4c02c1a42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596276390\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172186802475\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the first row, the right column contains the expression y times y minus 2, with y minus 2 in parentheses. Two red arrows extend from the coefficient y, terminating at the y and minus 2 in parentheses. In the second row, the text in the left column says \u201cDistribute.\u201d In the right column is y times y minus y times 2. In the last row, the text in the left column says \u201cSimplify.\u201d In the right column is y squared minus 2y.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172186802496\" data-type=\"media\" data-alt=\"y times y minus 2. Two arrows extend from the coefficient y, terminating at the y and minus 2 in parentheses.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_002a_img_new.jpg\" alt=\"y times y minus 2. Two arrows extend from the coefficient y, terminating at the y and minus 2 in parentheses.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-473cfb7b9b22e76a0415d4004658f4c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#92;&#99;&#100;&#111;&#116;&#125;&#32;&#121;&#32;&#45;&#32;&#121;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#92;&#99;&#100;&#111;&#116;&#125;&#32;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"67\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9b8de2701ba5c9bfe43a445f9ccce454_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#50;&#45;&#50;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"57\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596374530\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596370378\" data-type=\"exercise\">\n<div id=\"fs-id1169596404931\" data-type=\"problem\">\n<p id=\"fs-id1169596255252\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9c5349862ce8d80eff8fa24dbe88c985_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"67\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596399324\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596370185\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-aa8e94a1f3001eddb940e175579d6c20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"58\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596302246\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596377033\" data-type=\"exercise\">\n<div id=\"fs-id1169596212720\" data-type=\"problem\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596212720\" data-type=\"problem\">\n<p id=\"fs-id1169596218283\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-87a389184e0e1e0fc66bdf38c31ea1c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#92;&#108;&#101;&#102;&#116;&#40;&#100;&#45;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596344342\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596220091\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c5152e952ee68a8f3b0ba9b831504749_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#100;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#49;&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"67\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596302246\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596377033\" data-type=\"exercise\">\n<div id=\"fs-id1169596344342\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596382289\" data-type=\"problem\">\n<p id=\"fs-id1169596310964\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1c1aabb8293441db9805f1012155b5fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#43;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596348801\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172184496242\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the first row, the right column contains the expression yx times 2x plus y, with 2x plus y in parentheses. Two red arrows extend from 7x, terminating at 2x and y. In the second row, the text in the left column says \u201cDistribute.\u201d In the right column is 7x times 2x plus 7x times y. In the last row, the text in the left column says \u201cSimplify.\u201d In the right column is 14x squared plus 7xy.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172184496262\" data-type=\"media\" data-alt=\"7 x times 2 x plus y. Two arrows extend from 7x, terminating at 2x and y.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_003a_img_new.jpg\" alt=\"7 x times 2 x plus y. Two arrows extend from 7x, terminating at 2x and y.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-22c5a585f8a1a3cf6687f40dc1a2cbde_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#92;&#99;&#100;&#111;&#116;&#125;&#32;&#50;&#120;&#32;&#43;&#32;&#55;&#120;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#92;&#99;&#100;&#111;&#116;&#125;&#32;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fad7af0b97ab9f878ea395f1fcf61970_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#120;&#94;&#50;&#32;&#43;&#32;&#55;&#120;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"84\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596317227\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596367197\" data-type=\"exercise\">\n<div id=\"fs-id1169596372008\" data-type=\"problem\">\n<p>Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8bf669a97d2abb6985c4908ec6217b6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#52;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596258487\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596370082\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3a449baee45ab3c2a54ab2863659e8fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#48;&#120;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596367934\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596344668\" data-type=\"exercise\">\n<div id=\"fs-id1169596393579\" data-type=\"problem\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596393579\" data-type=\"problem\">\n<p id=\"fs-id1169596557276\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d8801b8f16dcf9d786793a5d0db59e9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#112;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#112;&#43;&#114;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596374505\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596240521\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-16d6aa05e1f219bf186742ee8a309ca7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#112;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"81\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596367934\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596344668\" data-type=\"exercise\">\n<div id=\"fs-id1169596374505\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596244318\" data-type=\"problem\">\n<p id=\"fs-id1169596375441\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-93791a50560f16b3422c596b7bd8b539_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#121;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#121;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"144\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596402073\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172187836045\" class=\"unnumbered unstyled\" style=\"height: 84px\" summary=\"This figure has two columns. In the first row, the right column contains the expression negative 2y times 4y squared plus 3y minus 5, with 4y plus 3y minus 5 in parentheses. Three red arrows extend from negative 2y, terminating at 4y squared, 3y, and minus 5. In the second row, the text in the left column says \u201cDistribute.\u201d In the right column is negative 2y times 4y squared plus negative 2y times 3y minus negative 2y times 5. In the last row, the text in the left column says \u201cSimplify.\u201d In the right column is negative 8y cubed minus 6y squared plus 10y.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 48px\">\n<td style=\"height: 48px;width: 151.406px\"><\/td>\n<td style=\"height: 48px;width: 498.406px\"><span id=\"eip-id1172187836065\" data-type=\"media\" data-alt=\"Negative 2 y times 4 y squared plus 3 y minus 5. Three arrows extend from negative 2 y, terminating at 4 y squared, 3 y, and minus 5.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_004a_img_new.jpg\" alt=\"Negative 2 y times 4 y squared plus 3 y minus 5. Three arrows extend from negative 2 y, terminating at 4 y squared, 3 y, and minus 5.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 18px\">\n<td style=\"height: 18px;width: 151.406px\">Distribute.<\/td>\n<td style=\"height: 18px;width: 498.406px\"><span id=\"eip-id1172187836082\" data-type=\"media\" data-alt=\"Negative 2 y times 4 y squared plus negative 2 y times 3 y minus negative 2 y times 5.\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a039b853d89cab0ef52e20484334859c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#32;&#121;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#125;&#32;&#52;&#32;&#121;&#94;&#50;&#43;&#40;&#45;&#50;&#32;&#121;&#41;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#125;&#32;&#51;&#32;&#121;&#45;&#40;&#45;&#50;&#32;&#121;&#41;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#125;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"233\" style=\"vertical-align: -5px;\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 18px\">\n<td style=\"height: 18px;width: 151.406px\">Simplify.<\/td>\n<td style=\"height: 18px;width: 498.406px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e3aa89e680efb951a561810fcbfa1395_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#32;&#121;&#94;&#51;&#45;&#54;&#32;&#121;&#94;&#50;&#43;&#49;&#48;&#32;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"135\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596287620\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596555903\" data-type=\"exercise\">\n<div id=\"fs-id1169596298286\" data-type=\"problem\">\n<p id=\"fs-id1169596299296\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b26d5d83a5c3bac3fb404c4d4107ad5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#121;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#56;&#121;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"144\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596307171\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596279480\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c0ef2b3a4192edc507b8d7751e99238d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#45;&#50;&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#49;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"153\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596318095\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596393126\" data-type=\"exercise\">\n<div id=\"fs-id1169596338665\" data-type=\"problem\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596338665\" data-type=\"problem\">\n<p id=\"fs-id1169596396784\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-33ca3eb3aa7386f903cc66775612b766_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"142\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596288192\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596396920\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0fe157ec750295486811fd723c36b7e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#45;&#49;&#50;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#43;&#50;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"141\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596318095\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596393126\" data-type=\"exercise\">\n<div id=\"fs-id1169596288192\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596369884\" data-type=\"problem\">\n<p id=\"fs-id1169596382601\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b0ccf5d5133e2f1e6a06be2d4fc43601_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#120;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"133\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596369851\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172187703559\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the first row, the right column contains the expression 2x cubed times x squared minus 8x plus 1, with x squared minus 8x plus 1 in parentheses. Three red arrows extend from 2x cubed, terminating at x squared, minus 8x, and 1. In the second row, the text in the left column says \u201cDistribute.\u201d In the right column is 2x cubed times x squared plus 2x cubed times negative 8x plus 2x cubed times 1. In the last row, the text in the left column says \u201cSimplify.\u201d In the right column is 2x to the fifth power minus 16x to the fourth power plus 2x cubed.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187703580\" data-type=\"media\" data-alt=\"2 x cubed times x squared minus 8 x plus 1. Three arrows extend from 2 x cubed, terminating at x squared, minus 8 x, and 1.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_005a_img_new.jpg\" alt=\"2 x cubed times x squared minus 8 x plus 1. Three arrows extend from 2 x cubed, terminating at x squared, minus 8 x, and 1.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-10e25c9fe830c6911698019e77d59a95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#32;&#120;&#94;&#51;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#125;&#32;&#120;&#94;&#50;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#32;&#120;&#94;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#125;&#40;&#45;&#56;&#32;&#120;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#32;&#120;&#94;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#125;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"249\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ec56e5acb181d1da36403a71cba21771_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#32;&#120;&#94;&#53;&#45;&#49;&#54;&#32;&#120;&#94;&#52;&#43;&#50;&#32;&#120;&#94;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"132\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596344336\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596291588\" data-type=\"exercise\">\n<div id=\"fs-id1169596291590\" data-type=\"problem\">\n<p id=\"fs-id1169596308826\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b241433fd7bf4bbfac1118b3bba786c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"134\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596279063\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596310312\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b72b4897f2c2e17625cc3e538f5ff48e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#50;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"141\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596298449\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596397986\" data-type=\"exercise\">\n<div id=\"fs-id1169596397988\" data-type=\"problem\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596397988\" data-type=\"problem\">\n<p id=\"fs-id1169596363190\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f9aadbab689502d78c42a6b5d3a70293_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#97;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"152\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596292326\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596292328\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2e733d610b1bb85e9f1614fbc014d6b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#56;&#123;&#97;&#125;&#94;&#123;&#53;&#125;&#92;&#32;&#43;&#32;&#49;&#50;&#123;&#97;&#125;&#94;&#123;&#52;&#125;&#45;&#51;&#54;&#123;&#97;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"166\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596298449\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596397986\" data-type=\"exercise\">\n<div id=\"fs-id1169596292326\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596372850\" data-type=\"problem\">\n<p id=\"fs-id1169596372852\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-39ee213be55cd1706785719b361eba03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596302382\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172182437666\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the first row, the text in the left column says \u201cThe monomial is the second factor.\u201d The right column contains the expression x plus 3, in parentheses, times p. Two red arrows extend from the p, terminating at x and 3. In the second row, the text in the left column says \u201cDistribute.\u201d In the right column is x times p plus 3 times p. In the last row, the text in the left column says \u201cSimplify.\u201d In the right column is xp plus 3p.\" data-label=\"\">\n<tbody>\n<tr>\n<td>The monomial is the second factor.<\/td>\n<td><span id=\"eip-id1172182437688\" data-type=\"media\" data-alt=\"x plus 3, in parentheses, times p. Two arrows extend from the p, terminating at x and 3.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_006a_img_new.jpg\" alt=\"x plus 3, in parentheses, times p. Two arrows extend from the p, terminating at x and 3.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-99e7c57b28c519b0893bce7f1fe65d7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#125;&#32;&#112;&#32;&#43;&#32;&#51;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#125;&#32;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"68\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-98f65478facfa0b8e78fd427117bb364_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#112;&#43;&#51;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596320183\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596315710\" data-type=\"exercise\">\n<div id=\"fs-id1169596315712\" data-type=\"problem\">\n<p id=\"fs-id1169596315714\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bf61eba247c2b41907c342d3b06384c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596391243\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596391245\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-19cf62c7f36427db605fa81ed9dc3484_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#112;&#43;&#56;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596374701\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596374704\" data-type=\"exercise\">\n<div id=\"fs-id1169596370491\" data-type=\"problem\"><\/div>\n<div id=\"fs-id1169596499263\" data-type=\"solution\">\n<p id=\"fs-id1169596285946\">\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596370491\" data-type=\"problem\">\n<p id=\"fs-id1169596370493\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8b9d3e930e3e60838ee4aa0a0430ddd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596499263\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596285946\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c41b8a80f954761232859e0146edc137_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#112;&#43;&#52;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"58\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Multiply a Binomial by a Binomial<\/h1>\n<p id=\"fs-id1169596303931\">Just like there are different ways to represent multiplication of numbers, there are several methods that can be used to multiply a <span class=\"no-emphasis\" data-type=\"term\">binomial<\/span> times a binomial. We will start by using the Distributive Property.<\/p>\n<h1 data-type=\"title\">Multiply a Binomial by a Binomial Using the Distributive Property<\/h1>\n<p id=\"fs-id1169596286032\">Look at the table below, where we multiplied a binomial by a <span class=\"no-emphasis\" data-type=\"term\">monomial<\/span>.<\/p>\n<table id=\"eip-id1172186695524\" class=\"grid\" summary=\"This figure has two columns. In the first row, the right column contains the expression x plus 3, in parentheses, times p. Two red arrows extend from the p, terminating at x and 3. In the second row, the text in the left column says \u201cWe distributed the p to get\u201d. The right column contains xp plus 3p. In the third row, the text in the left column says \u201cWhat if we have x plus 7 instead of p?\u201d In the right column is the product of two binomials, x plus 3 and x plus 7. Two red arrows extend from x plus 7, terminating at the x and the 3 in the first binomial. In the fourth row, the text in the left column says \u201cThink of the x plus 7 as the p above.\u201d In the right column is x times x plus 7 plus 3 times x plus 7, where x plus 7 is in parentheses twice. In the fifth row, the text in the left column says \u201cDistribute x plus 7.\u201d In the right column is x squared plus 7x plus 3x plus 21. In the sixth row, the text in the left column says \u201cCombine like terms.\u201d In the right column is x squared plus 10x plus 21.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172186695544\" data-type=\"media\" data-alt=\"x plus 3, in parentheses, times p. Two arrows extend from the p, terminating at x and 3.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_007a_img_new.jpg\" alt=\"x plus 3, in parentheses, times p. Two arrows extend from the p, terminating at x and 3.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We distributed the <em data-effect=\"italics\">p<\/em> to get:<\/td>\n<td><span id=\"eip-id1172186695561\" data-type=\"media\" data-alt=\"x p plus 3 p.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_007b_img_new.jpg\" alt=\"x p plus 3 p.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>What if we have (<em data-effect=\"italics\">x<\/em> + 7) instead of <em data-effect=\"italics\">p<\/em>?<\/td>\n<td><span id=\"eip-id1172186695577\" data-type=\"media\" data-alt=\"x plus 3 multiplied by x plus 7. Two arrows extend from x plus 7, terminating at the x and the 3 in the first binomial.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_007c_img_new.jpg\" alt=\"x plus 3 multiplied by x plus 7. Two arrows extend from x plus 7, terminating at the x and the 3 in the first binomial.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute (<em data-effect=\"italics\">x<\/em> + 7).<\/td>\n<td><span id=\"eip-id1172182437009\" data-type=\"media\" data-alt=\"The sum of two products. The product of x and x plus 7, plus the product of 3 and x plus 7.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_007d_img_new.jpg\" alt=\"The sum of two products. The product of x and x plus 7, plus the product of 3 and x plus 7.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute again.<\/td>\n<td><span id=\"eip-id1172182437026\" data-type=\"media\" data-alt=\"x squared plus 7 x plus 3 x plus 21.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_007e_img_new.jpg\" alt=\"x squared plus 7 x plus 3 x plus 21.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1172182437043\" data-type=\"media\" data-alt=\"x squared plus 10 x plus 21.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_007f_img_new.jpg\" alt=\"x squared plus 10 x plus 21.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596344846\">Notice that before combining like terms, you had four terms. You multiplied the two terms of the first binomial by the two terms of the second binomial\u2014four multiplications.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596458020\" data-type=\"problem\">\n<p id=\"fs-id1169596458022\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3c64f4131d08b416bbeea29d2ec29880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596308212\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172185589112\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the first row, the right column contains the product of two binomials, y plus 5 and y plus 8. Two arrows extend from y plus 8, terminating at the y and 5 in the first binomial. In the second row, the text in the left column says \u201cDistribute y plus 8.\u201d The right column contains y times y plus 8 plus 5 times y plus 8, where y plus 8 is in parentheses twice. In the third row, the text in the left column says \u201cDistribute again.\u201d In the right column is y squared plus 8y plus 5y plus 40. In the last row, the text in the left column says \u201cCombine like terms.\u201d In the right column is y squared plus 13y plus 40.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187708587\" data-type=\"media\" data-alt=\"The product of two binomials, y plus 5 and y plus 8. Two arrows extend from y plus 8, terminating at the y and the 5 in the first binomial.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_008a_img_new.jpg\" alt=\"The product of two binomials, y plus 5 and y plus 8. Two arrows extend from y plus 8, terminating at the y and the 5 in the first binomial.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute (<em data-effect=\"italics\">y<\/em> + 8).<\/td>\n<td><span id=\"eip-id1172187708604\" data-type=\"media\" data-alt=\"The sum of two products, the product of y and y plus 8, plus the product of 5 and y plus 8.\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fe410fb70da8fb89c25fb97ea43972ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#40;&#121;&#43;&#56;&#41;&#125;&#125;&#43;&#53;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#40;&#121;&#43;&#56;&#41;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -5px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute again<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f3f562776948173cd5283bc52ba5601a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#92;&#99;&#100;&#111;&#116;&#125;&#125;&#32;&#121;&#32;&#43;&#121;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#92;&#99;&#100;&#111;&#116;&#125;&#125;&#32;&#56;&#32;&#43;&#32;&#53;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#92;&#99;&#100;&#111;&#116;&#125;&#125;&#32;&#121;&#32;&#43;&#32;&#53;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#92;&#99;&#100;&#111;&#116;&#125;&#125;&#32;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"158\" style=\"vertical-align: -4px;\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2dc02a96c9b81bcf55a179def1ebeec5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#50;&#43;&#56;&#32;&#121;&#43;&#53;&#32;&#121;&#43;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5eda29745b237381c54d867498365655_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#50;&#43;&#49;&#51;&#32;&#121;&#43;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5917ccdee92526bf7968c6f07c240696_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<div id=\"fs-id1169596291728\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596291732\" data-type=\"exercise\">\n<div id=\"fs-id1169596499248\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596499251\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f80d0f75bef8bfa4a92cd8f578ee16e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#55;&#120;&#43;&#55;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"106\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596360795\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596360798\" data-type=\"exercise\">\n<div id=\"fs-id1169596360800\" data-type=\"problem\"><\/div>\n<div id=\"fs-id1169596375449\" data-type=\"solution\">\n<p id=\"fs-id1169596348525\">\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596360800\" data-type=\"problem\">\n<p id=\"fs-id1169596366221\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ea110ffd4b0c662c1020a64f368a09b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#120;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596375449\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596348525\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-373ac2b442cb7c4b5619e943f086a58c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#49;&#120;&#43;&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"125\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596360795\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596360798\" data-type=\"exercise\">\n<div id=\"fs-id1169596375449\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596402877\" data-type=\"problem\">\n<p id=\"fs-id1169596402879\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-628097ffbb8a642d553a128fc703ea79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#121;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#121;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596303688\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172187825290\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the first row, the right column contains the product of two binomials, 2y plus 5 and 3y plus 4. Two arrows extend from 3y plus 4, terminating at 2y and 5 in the first binomial. In the second row, the text in the left column says \u201cDistribute 3y plus 4.\u201d The right column contains 2y times 3y plus 4 plus 5 times 3y plus 4, where 3y plus 4 is in parentheses twice. In the third row, the text in the left column says \u201cDistribute again.\u201d In the right column is 6y squared plus 8y plus 15y plus 20. In the last row, the text in the left column says \u201cCombine like terms.\u201d In the right column is 6y squared plus 23y plus 20.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187825310\" data-type=\"media\" data-alt=\"The product of two binomials, 2 y plus 5 and 3 y plus 4. Two arrows extend from 3y plus 4, terminating at 2y and 5 in the first binomial.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_009a_img_new.jpg\" alt=\"The product of two binomials, 2 y plus 5 and 3 y plus 4. Two arrows extend from 3y plus 4, terminating at 2y and 5 in the first binomial.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute (3<em data-effect=\"italics\">y<\/em> + 4).<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6d513c4bd2f254eb2e5acc1b17b0d466_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#32;&#121;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#40;&#51;&#32;&#121;&#43;&#52;&#41;&#125;&#43;&#53;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#40;&#51;&#32;&#121;&#43;&#52;&#41;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"173\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Distribute again<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-da5e812bdf3fbecd7c50eaad0aa5292a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#121;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#92;&#99;&#100;&#111;&#116;&#125;&#125;&#32;&#51;&#121;&#32;&#43;&#32;&#50;&#121;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#92;&#99;&#100;&#111;&#116;&#125;&#125;&#32;&#52;&#32;&#43;&#32;&#53;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#92;&#99;&#100;&#111;&#116;&#125;&#125;&#32;&#51;&#121;&#32;&#43;&#32;&#53;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#92;&#99;&#100;&#111;&#116;&#125;&#125;&#32;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"193\" style=\"vertical-align: -4px;\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c6b75764908fa45f6cf3f9b6b450d6ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#32;&#121;&#94;&#50;&#43;&#56;&#32;&#121;&#43;&#49;&#53;&#32;&#121;&#43;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"154\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c6d729e383128422bcafbb959d3bc129_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#32;&#121;&#94;&#50;&#43;&#50;&#51;&#32;&#121;&#43;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"114\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596286465\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596286279\" data-type=\"exercise\">\n<div id=\"fs-id1169596286281\" data-type=\"problem\">\n<p id=\"fs-id1169596286284\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f0827760824b25e0a7a22e5d9f56784a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#98;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#98;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"123\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596286011\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596286013\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7f01ae75ada684f82e2e58859ed4a180_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#56;&#98;&#43;&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"119\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596286306\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596286309\" data-type=\"exercise\">\n<div id=\"fs-id1169596286311\" data-type=\"problem\"><\/div>\n<div id=\"fs-id1169596374723\" data-type=\"solution\">\n<p id=\"fs-id1169596285411\">\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596286311\" data-type=\"problem\">\n<p id=\"fs-id1169596286755\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-32aa97c7c30e1e512e7c7a5625228d34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596374723\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596285411\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4680c71d4a067d59118f4d9b65a21bd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#55;&#97;&#43;&#55;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"105\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596286306\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596286309\" data-type=\"exercise\">\n<div id=\"fs-id1169596374723\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1169596367035\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-48f5cb521f42e7b9a46f765e3ff48015_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#121;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#121;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596360324\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172181066482\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the first row, the right column contains the product of two binomials, 4y plus 3 and 2y minus 5. Two arrows extend from 2y minus 5, terminating at 4y and 3 in the first binomial. In the second row, the text in the left column says \u201cDistribute.\u201d The right column contains 4y times 2y minus 5 plus 3 times 2y minus 5, where 2y minus 5 is in parentheses twice. In the third row, the text in the left column says \u201cDistribute again.\u201d In the right column is 8y squared minus 20y plus 6y minus 15. In the last row, the text in the left column says \u201cCombine like terms.\u201d In the right column is 8y squared minus 14y minus 15.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172181066502\" data-type=\"media\" data-alt=\"The product of two binomials, 4y plus 3 and 2 y minus 5. Two arrows extend from 2y minus 5, terminating at 4 y and 3 in the first binomial.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_010a_img_new.jpg\" alt=\"The product of two binomials, 4y plus 3 and 2 y minus 5. Two arrows extend from 2y minus 5, terminating at 4 y and 3 in the first binomial.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-93290769de31799ed15a86efa4b13249_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#32;&#121;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#40;&#50;&#32;&#121;&#45;&#53;&#41;&#125;&#125;&#43;&#51;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#40;&#50;&#32;&#121;&#45;&#53;&#41;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"173\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Distribute again.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-43d8a754d4936af980036872de02f17f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#121;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#92;&#99;&#100;&#111;&#116;&#125;&#125;&#32;&#50;&#121;&#32;&#43;&#32;&#52;&#121;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#92;&#99;&#100;&#111;&#116;&#125;&#125;&#32;&#40;&#45;&#53;&#41;&#32;&#43;&#32;&#51;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#92;&#99;&#100;&#111;&#116;&#125;&#125;&#32;&#50;&#121;&#32;&#43;&#32;&#51;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#92;&#99;&#100;&#111;&#116;&#125;&#125;&#32;&#40;&#45;&#53;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"248\" style=\"vertical-align: -5px;\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-487bfd80dcfa026b580886a1940c4ec1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#32;&#121;&#94;&#50;&#45;&#50;&#48;&#32;&#121;&#43;&#54;&#32;&#121;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"153\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0c1382b804878106afaa2ae3406c5649_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#32;&#121;&#94;&#50;&#45;&#49;&#52;&#32;&#121;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"113\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596386394\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596348839\" data-type=\"exercise\">\n<div id=\"fs-id1169596348842\" data-type=\"problem\">\n<p id=\"fs-id1169596348844\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-48e98167423f1b85b26101136e07fce2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#121;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#121;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596391031\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596401314\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-01b9c61ac6b026028e76a5fdc54e26c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#121;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596392758\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596392762\" data-type=\"exercise\">\n<div id=\"fs-id1169596360936\" data-type=\"problem\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596360936\" data-type=\"problem\">\n<p id=\"fs-id1169596360938\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f15bc178db135cbdcb304f6df328a7ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#99;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#99;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"123\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596397978\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596397980\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-17cf3ef491e1e6029f542ec4998d4bae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#52;&#99;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"110\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596392758\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596392762\" data-type=\"exercise\">\n<div id=\"fs-id1169596397978\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596401560\" data-type=\"problem\">\n<p id=\"fs-id1169596401562\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-85d27e8da288724b5ccfa73152d018fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596378360\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172182438454\" class=\"unnumbered unstyled\" style=\"height: 90px; width: 100%;\" summary=\"This figure has two columns. In the first row, the right column contains the product of two binomials, x minus 2 and x minus y. Two arrows extend from x minus y, terminating at x and 2 in the first binomial. In the second row, the text in the left column says \u201cDistribute.\u201d The right column contains x times x minus y minus 2 times x minus y, where x minus y is in parentheses twice. In the third row, the text in the left column says \u201cDistribute again.\u201d In the right column is x squared minus xy minus 2x plus 2y. In the last row, the text in the left column says \u201cThere are no like terms to combine.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172182438474\" data-type=\"media\" data-alt=\"The product of two binomials, x minus 2 and x minus y. Two arrows extend from x minus y, terminating at x and 2 in the first binomial.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_011a_img_new.jpg\" alt=\"The product of two binomials, x minus 2 and x minus y. Two arrows extend from x minus y, terminating at x and 2 in the first binomial.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e02876e45b1d02c6a86bb1f6e0f8db20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#40;&#120;&#45;&#121;&#41;&#125;&#125;&#45;&#50;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#40;&#120;&#45;&#121;&#41;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"150\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Distribute again.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c6b8d7aefc2358195a08d49629a5e4ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#92;&#99;&#100;&#111;&#116;&#125;&#125;&#32;&#40;&#120;&#41;&#32;&#43;&#32;&#120;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#92;&#99;&#100;&#111;&#116;&#125;&#125;&#32;&#40;&#45;&#121;&#41;&#32;&#43;&#32;&#40;&#45;&#50;&#41;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#92;&#99;&#100;&#111;&#116;&#125;&#125;&#32;&#40;&#120;&#41;&#32;&#43;&#32;&#40;&#45;&#50;&#41;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#92;&#99;&#100;&#111;&#116;&#125;&#125;&#32;&#40;&#45;&#121;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"299\" style=\"vertical-align: -5px;\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-528bfafe9a8e8b6d5e18659c53881d50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#94;&#50;&#45;&#120;&#32;&#121;&#45;&#50;&#32;&#120;&#43;&#50;&#32;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"139\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>There are no like terms to combine.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-528bfafe9a8e8b6d5e18659c53881d50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#94;&#50;&#45;&#120;&#32;&#121;&#45;&#50;&#32;&#120;&#43;&#50;&#32;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"139\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596375029\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596375033\" data-type=\"exercise\">\n<div id=\"fs-id1169596375035\" data-type=\"problem\">\n<p id=\"fs-id1169596375037\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5173e2953c68eeeed3ea318600a99ab3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#45;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596373985\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596373987\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c65c3778b7891fc8998d643084fceb33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#45;&#97;&#98;&#43;&#55;&#97;&#45;&#55;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"134\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596384881\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596393617\" data-type=\"exercise\">\n<div id=\"fs-id1169596393619\" data-type=\"problem\"><\/div>\n<div id=\"fs-id1169596398460\" data-type=\"solution\">\n<p id=\"fs-id1169596558190\">\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596393619\" data-type=\"problem\">\n<p id=\"fs-id1169596393621\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-539a6a6720f8c67d5baed9df84d93e10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596398460\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596558190\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0ea3deb5ba455c101e58779255cbee31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#120;&#121;&#43;&#53;&#120;&#45;&#53;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"139\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Multiply a Binomial by a Binomial Using the FOIL Method<\/h1>\n<p id=\"fs-id1169596308783\">Remember that when you multiply a binomial by a binomial you get four terms. Sometimes you can combine like terms to get a <span class=\"no-emphasis\" data-type=\"term\">trinomial<\/span>, but sometimes, like in the above example, there are no like terms to combine.<\/p>\n<p id=\"fs-id1169596556140\">Let\u2019s look at the last example again and pay particular attention to how we got the four terms.<\/p>\n<div id=\"fs-id1169596556146\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-842f1ea8ca255540b3e086268d0ff7bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#120;&#121;&#45;&#50;&#120;&#43;&#50;&#121;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"139\" style=\"vertical-align: -15px;\" \/><\/div>\n<p id=\"fs-id1169596388950\">Where did the first term, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-60a826196aae662bd64e5dd6bbd1fafd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/>, come from?<\/p>\n<p><span id=\"fs-id1169596298873\" data-type=\"media\" data-alt=\"This figure explains how to multiply a binomial using the FOIL method. It has two columns, with written instructions on the left and math on the right. At the top of the figure, the text in the left column says \u201cIt is the product of x and x, the first terms in x minus 2 and x minus y.\u201d In the right column is the product of x minus 2 and x minus y. An arrow extends from the x in x minus 2, and terminates at the x in x minus y. Below this is the word \u201cFirst.\u201d One row down, the text in the left column says \u201cThe next terms, negative xy, is the product of x and negative y, the two outer terms.\u201d In the right column is the product of x minus 2 and x minus y, with another arrow extending from the x in x minus 2 to the y in x minus y. Below this is the word \u201cOuter.\u201d One row down, the text in the left column says \u201cThe third term, negative 2 x, is the product of negative 2 and x, the two inner terms.\u201d In the right column is the product of x minus 2 and x minus y with a third arrow extending from minus 2 in x minus 2 and terminating at the x in x minus y. Below this is the word \u201cInner.\u201d In the last row, the text in the left column says \u201cAnd the last term, plus 2y, came from multiplying the two last terms, negative 2 and negative y.\u201d In the right column is the product of x minus 2 and x minus y, with a fourth arrow extending from the minus 2 in x minus 2 to the minus y in x minus y. Below this is the word \u201cLast.\u201d\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_012_img_new.jpg\" alt=\"This figure explains how to multiply a binomial using the FOIL method. It has two columns, with written instructions on the left and math on the right. At the top of the figure, the text in the left column says \u201cIt is the product of x and x, the first terms in x minus 2 and x minus y.\u201d In the right column is the product of x minus 2 and x minus y. An arrow extends from the x in x minus 2, and terminates at the x in x minus y. Below this is the word \u201cFirst.\u201d One row down, the text in the left column says \u201cThe next terms, negative xy, is the product of x and negative y, the two outer terms.\u201d In the right column is the product of x minus 2 and x minus y, with another arrow extending from the x in x minus 2 to the y in x minus y. Below this is the word \u201cOuter.\u201d One row down, the text in the left column says \u201cThe third term, negative 2 x, is the product of negative 2 and x, the two inner terms.\u201d In the right column is the product of x minus 2 and x minus y with a third arrow extending from minus 2 in x minus 2 and terminating at the x in x minus y. Below this is the word \u201cInner.\u201d In the last row, the text in the left column says \u201cAnd the last term, plus 2y, came from multiplying the two last terms, negative 2 and negative y.\u201d In the right column is the product of x minus 2 and x minus y, with a fourth arrow extending from the minus 2 in x minus 2 to the minus y in x minus y. Below this is the word \u201cLast.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596497182\">We abbreviate \u201cFirst, Outer, Inner, Last\u201d as FOIL. The letters stand for \u2018<strong data-effect=\"bold\">F<\/strong>irst, <strong data-effect=\"bold\">O<\/strong>uter, <strong data-effect=\"bold\">I<\/strong>nner, <strong data-effect=\"bold\">L<\/strong>ast\u2019. The word FOIL is easy to remember and ensures we find all four products.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-2040 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/FOIL-300x142.png\" alt=\"FOIL image\" width=\"300\" height=\"142\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/FOIL-300x142.png 300w, https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/FOIL-65x31.png 65w, https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/FOIL-225x106.png 225w, https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/FOIL-350x165.png 350w, https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/FOIL.png 423w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8ae3cb2196ded81704cac30594e9079b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#120;&#45;&#50;&#41;&#40;&#120;&#45;&#121;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7293f41c8187c1343427e26b0d39a850_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#109;&#97;&#116;&#114;&#105;&#120;&#125;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#32;&#120;&#121;&#45;&#32;&#50;&#120;&#43;&#32;&#50;&#121;&#32;&#92;&#92;&#32;&#70;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#101;&#110;&#115;&#112;&#97;&#99;&#101;&#32;&#79;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#101;&#110;&#115;&#112;&#97;&#99;&#101;&#32;&#73;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#101;&#110;&#115;&#112;&#97;&#99;&#101;&#32;&#76;&#32;&#92;&#101;&#110;&#100;&#123;&#109;&#97;&#116;&#114;&#105;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"139\" style=\"vertical-align: -11px;\" \/><\/p>\n<p id=\"fs-id1169596308801\">Let\u2019s look at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8a87362ad430297701f168ff50c58615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<table id=\"eip-id1172181067051\" class=\"grid\" summary=\"This figure compares using the distributive property to using the FOIL method for multiplying the binomials x plus 3 and x plus 7. The figure has two columns. Written at the top of the left column is \u201cDistributive Property. Below this is the product of x plus 3 and x plus 7. Below this is x times x plus 7 plus 3 times x plus 7, where x plus 7 is in parentheses twice. Below this is x squared plus 7x plus 3x plus 21. Below x squared is the letter F, below 7x is the letter O, below 3x is the letter I, and below 21 is the letter L, spelling FOIL. Below this is the expression with like terms combined: x squared plus 10x plus 21. Written at the top of the right column is \u201cFOIL.\u201d Below this is the product of x plus 3 and x plus y. An arrow extends from the x in x plus 3 to the x in x plus 7. A second arrow extends from the x in x plus 3 to the 7 in x plus 7. A third arrow extends from the 3 in x plus 3 to the x in x plus 7. A fourth arrow extends from the 3 in x plus 3 to the 7 in x plus 7. Below this is the same expression arrived at through the distributive property in the left column: x squared plus 7x plus 3x plus 21, with the letter F below x squared, the letter O below 7x, the letter I below 3x, and the letter L below 21. Below this is the expression with like terms combined once more: x squared plus 10x plus 21.\" data-label=\"\">\n<tbody>\n<tr>\n<td data-align=\"center\">Distibutive Property<\/td>\n<td data-align=\"center\">FOIL<\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1172181067077\" data-type=\"media\" data-alt=\"The product of x plus 3 and x plus 7.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_022a_img_new.jpg\" alt=\"The product of x plus 3 and x plus 7.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1172181067088\" data-type=\"media\" data-alt=\"The product of x plus 3 and x plus y. An arrow extends from the x in x plus 3 to the x in x plus 7. A second arrow extends from the x in x plus 3 to the 7 in x plus 7. A third arrow extends from the 3 in x plus 3 to the x in x plus 7. A fourth arrow extends from the 3 in x plus 3 to the 7 in x plus 7.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_022e_img_new.jpg\" alt=\"The product of x plus 3 and x plus y. An arrow extends from the x in x plus 3 to the x in x plus 7. A second arrow extends from the x in x plus 3 to the 7 in x plus 7. A third arrow extends from the 3 in x plus 3 to the x in x plus 7. A fourth arrow extends from the 3 in x plus 3 to the 7 in x plus 7.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1172181067102\" data-type=\"media\" data-alt=\"The sum of two products, the product of x and x plus 7, and the product of 3 and x plus 7.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_022b_img_new.jpg\" alt=\"The sum of two products, the product of x and x plus 7, and the product of 3 and x plus 7.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1172181067118\" data-type=\"media\" data-alt=\"x squared plus 7 x plus 3 x plus 21. Below x squared is the letter F, below 7 x is the letter O, below 3 x is the letter I, and below 21 is the letter L, spelling FOIL.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_022c_img_new.jpg\" alt=\"x squared plus 7 x plus 3 x plus 21. Below x squared is the letter F, below 7 x is the letter O, below 3 x is the letter I, and below 21 is the letter L, spelling FOIL.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1172181067128\" data-type=\"media\" data-alt=\"x squared plus 7 x plus 3 x plus 21. Below x squared is the letter F, below 7 x is the letter O, below 3 x is the letter I, and below 21 is the letter L, spelling FOIL.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_022f_img_new.jpg\" alt=\"x squared plus 7 x plus 3 x plus 21. Below x squared is the letter F, below 7 x is the letter O, below 3 x is the letter I, and below 21 is the letter L, spelling FOIL.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1172181067142\" data-type=\"media\" data-alt=\"x squared plus 10 x plus 21.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_022d_img_new.jpg\" alt=\"x squared plus 10 x plus 21.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1172181067153\" data-type=\"media\" data-alt=\"x squared plus 10 x plus 21.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_022g_img_new.jpg\" alt=\"x squared plus 10 x plus 21.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596376847\">Notice how the terms in third line fit the FOIL pattern.<\/p>\n<p id=\"fs-id1169596376850\">Now we will do an example where we use the FOIL pattern to multiply two binomials.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">How to Multiply a Binomial by a Binomial using the FOIL Method<\/div>\n<div id=\"fs-id1169596376856\" data-type=\"exercise\">\n<div id=\"fs-id1169596276394\" data-type=\"problem\">\n<p id=\"fs-id1169596276399\">Multiply using the FOIL method: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-90e1fc428ee631ccaee28a8e8438b337_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596361161\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solutio<\/strong><strong>n<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse;width: 100%;height: 274px\">\n<tbody>\n<tr style=\"height: 16px\">\n<td style=\"width: 101.325%;height: 16px;text-align: center\" colspan=\"3\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-90e1fc428ee631ccaee28a8e8438b337_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 54px\">\n<td style=\"width: 36.9258%;height: 54px\"><strong>Step 1.<\/strong><br \/>\nMultiply the <em data-effect=\"italics\"><span style=\"color: #ff0000\">First<\/span>\u00a0<\/em>terms, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3a6952216199da24082e50f15ef84000_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#120;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"33\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 16.4312%;height: 54px\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2685\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_1.jpg\" alt=\"the product of binomials x plus 5 and x plus 9. Below this is the product of x plus 5 and x plus 9 again, with an arrow extending from the x in the first binomial to the x in the second binomial.\" width=\"110\" height=\"53\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_1.jpg 172w, https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_1-65x31.jpg 65w\" sizes=\"auto, (max-width: 110px) 100vw, 110px\" \/><\/a><\/td>\n<td style=\"width: 47.9682%;height: 54px\">\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6757c265581d364bd5d7475d51b6dbdb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#120;&#94;&#50;&#125;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#38; &#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#92;&#92;&#32;&#70;&#32;&#38;&#32;&#38;&#32;&#79;&#32;&#38;&#32;&#38;&#32;&#73;&#32;&#38;&#32;&#38;&#32;&#76;&#32;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"226\" style=\"vertical-align: -11px;\" \/><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 54px\">\n<td style=\"width: 36.9258%;height: 54px\"><strong>Step 2.<\/strong><br \/>\nMultiply the <em data-effect=\"italics\"><span style=\"color: #ff0000\">Outer<\/span>\u00a0<\/em>terms, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a7d236bff3255a7f59ff4f8d1611a067_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#120;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#57;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"32\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 16.4312%;height: 54px\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_2.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2686\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_2.jpg\" alt=\"the product of x plus 5 and x plus 9 again, with an arrow extending from x in the first binomial to the 9 in the second binomial.\" width=\"110\" height=\"41\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_2.jpg 182w, https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_2-65x24.jpg 65w\" sizes=\"auto, (max-width: 110px) 100vw, 110px\" \/><\/a><\/td>\n<td style=\"width: 47.9682%;height: 54px;text-align: center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f67c701c87f04639f01de2d4349616f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#120;&#94;&#50;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#43;&#125;&#125;&#32;&#38;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#57;&#120;&#125;&#125;&#32;&#38; &#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#92;&#92;&#32;&#70;&#32;&#38;&#32;&#38;&#32;&#79;&#32;&#38;&#32;&#38;&#32;&#73;&#32;&#38;&#32;&#38;&#32;&#76;&#32;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"222\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 66px\">\n<td style=\"width: 36.9258%;height: 66px\"><strong>Step 3.<\/strong><br \/>\nMultiply the <span style=\"color: #ff0000\"><em data-effect=\"italics\">Inner <\/em><\/span>terms, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1a3bc25aed0113ae15f9ceafac82270b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#53;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"32\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 16.4312%;height: 66px\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_3.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2687\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_3.jpg\" alt=\"contains the product of x plus 5 and x plus 9 again, with an arrow extending from 5 in the first binomial to the x in the second binomial.\" width=\"110\" height=\"39\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_3.jpg 176w, https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_3-65x23.jpg 65w\" sizes=\"auto, (max-width: 110px) 100vw, 110px\" \/><\/a><\/td>\n<td style=\"width: 47.9682%;height: 66px;text-align: center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bc662452a0ef0a085152e91f638e4d06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#120;&#94;&#50;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#57;&#120;&#32;&#38; &#43;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#53;&#120;&#125;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#92;&#92;&#32;&#70;&#32;&#38;&#32;&#38;&#32;&#79;&#32;&#38;&#32;&#38;&#32;&#73;&#32;&#38;&#32;&#38;&#32;&#76;&#32;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"218\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 68px\">\n<td style=\"width: 36.9258%;height: 68px\"><strong>Step 4.<\/strong><br \/>\nMultiply the<span style=\"color: #ff0000\"> <em data-effect=\"italics\">Last <\/em><\/span>terms, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dc7a849b1f3d861ac412d3ab4cef1246_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#53;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#57;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 16.4312%;height: 68px\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_4.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2688\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_4.jpg\" alt=\"the product of x plus 5 and x plus 9 again, with an arrow extending from 5 in the first binomial to 9 in the second binomial.\" width=\"110\" height=\"46\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_4.jpg 187w, https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex11_4-65x27.jpg 65w\" sizes=\"auto, (max-width: 110px) 100vw, 110px\" \/><\/a><\/td>\n<td style=\"width: 47.9682%;height: 68px;text-align: center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7c997221ffe25a3926497f0d58f884b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#120;&#94;&#50;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#57;&#120;&#32;&#38; &#43;&#32;&#38;&#32;&#53;&#120;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#43;&#125;&#125;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#52;&#53;&#125;&#125;&#32;&#92;&#92;&#32;&#70;&#32;&#38;&#32;&#38;&#32;&#79;&#32;&#38;&#32;&#38;&#32;&#73;&#32;&#38;&#32;&#38;&#32;&#76;&#32;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"211\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 36.9258%;height: 16px\"><strong>Step 5.<\/strong> Combine like terms.<\/td>\n<td style=\"width: 16.4312%;height: 16px\"><\/td>\n<td style=\"width: 47.9682%;height: 16px;text-align: center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a6971abb33521111e3bb301e6e8c8a06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#94;&#50;&#43;&#49;&#52;&#120;&#43;&#52;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"106\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596398431\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596398435\" data-type=\"exercise\">\n<div id=\"fs-id1169596398437\" data-type=\"problem\">\n<p id=\"fs-id1169596398439\">Multiply using the FOIL method: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-093e34d4ea120abd3984476fc21627b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596360980\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596360982\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3adc54339bb5fe36943d63780aade741_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#52;&#120;&#43;&#52;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"107\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596405489\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596405493\" data-type=\"exercise\">\n<div id=\"fs-id1169596405495\" data-type=\"problem\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596405495\" data-type=\"problem\">\n<p id=\"fs-id1169596405497\">Multiply using the FOIL method: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2da7a5ed1469ba85aa137ca2554b3f59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#49;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596364325\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596364327\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b1dd799eda4e7bcb395154e0fc1e9d63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#48;&#121;&#43;&#53;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>We summarize the steps of the FOIL method below. The FOIL method only applies to multiplying binomials, not other polynomials!<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Multiply two binomials using the FOIL method<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><span id=\"fs-id1171792521436\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_026_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596450761\">When you multiply by the FOIL method, drawing the lines will help your brain focus on the pattern and make it easier to apply.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596450770\" data-type=\"problem\">\n<p id=\"fs-id1169596450772\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-46edb7b43893b93fb6823d6e20167b0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596365991\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse;width: 100%;height: 274px\">\n<tbody>\n<tr style=\"height: 16px\">\n<td style=\"width: 101.325%;height: 16px;text-align: right\" colspan=\"3\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-46edb7b43893b93fb6823d6e20167b0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 54px\">\n<td style=\"width: 36.9258%;height: 54px\">Multiply the <em data-effect=\"italics\"><span style=\"color: #ff0000\">First<\/span>\u00a0<\/em>terms, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-74a66af7e76871cd43e5c92f54ab8952_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#121;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#121;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 16.4312%;height: 54px\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2678\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_1.jpg\" alt=\"This image shows the product of two binomials, y minus 7 and y plus 4, with an arrow extending from the y in the first binomial to the y in the second binomial.\" width=\"110\" height=\"44\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_1.jpg 115w, https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_1-65x26.jpg 65w\" sizes=\"auto, (max-width: 110px) 100vw, 110px\" \/><\/a><\/td>\n<td style=\"width: 47.9682%;height: 54px\">\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d7d9ef47855e1e41dbd15569ad3e9155_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#121;&#94;&#50;&#125;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#38; &#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#92;&#92;&#32;&#70;&#32;&#38;&#32;&#38;&#32;&#79;&#32;&#38;&#32;&#38;&#32;&#73;&#32;&#38;&#32;&#38;&#32;&#76;&#32;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"226\" style=\"vertical-align: -11px;\" \/><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 54px\">\n<td style=\"width: 36.9258%;height: 54px\">Multiply the <em data-effect=\"italics\"><span style=\"color: #ff0000\">Outer<\/span>\u00a0<\/em>terms, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6d270923d0c72d199fdf51651e94c6d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#121;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"31\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 16.4312%;height: 54px\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_2.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2679\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_2.jpg\" alt=\"This image shows the product of y minus 7 and y plus 4 again, with a second arrow extending from y in the first binomial to 4 in the second binomial.\" width=\"110\" height=\"55\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_2.jpg 115w, https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_2-65x33.jpg 65w\" sizes=\"auto, (max-width: 110px) 100vw, 110px\" \/><\/a><\/td>\n<td style=\"width: 47.9682%;height: 54px;text-align: center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a744169c140bd9ddd1c5293f516c4394_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#121;&#94;&#50;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#43;&#125;&#125;&#32;&#38;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#52;&#121;&#125;&#125;&#32;&#38; &#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#92;&#92;&#32;&#70;&#32;&#38;&#32;&#38;&#32;&#79;&#32;&#38;&#32;&#38;&#32;&#73;&#32;&#38;&#32;&#38;&#32;&#76;&#32;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"221\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 66px\">\n<td style=\"width: 36.9258%;height: 66px\">Multiply the <span style=\"color: #ff0000\"><em data-effect=\"italics\">Inner <\/em><\/span>terms, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1132c344f2c36a9a06102e1abf43cf5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#45;&#55;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#121;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 16.4312%;height: 66px\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_3.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2680\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_3.jpg\" alt=\"This image shows the product of y minus 7 and y plus 4 again, with a third arrow extending from the minus 7 in the first binomial to the y in the second binomial.\" width=\"110\" height=\"71\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_3.jpg 117w, https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_3-65x42.jpg 65w\" sizes=\"auto, (max-width: 110px) 100vw, 110px\" \/><\/a><\/td>\n<td style=\"width: 47.9682%;height: 66px;text-align: center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bdb52962fea06c9fe6f298d66af12e70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#121;&#94;&#50;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#52;&#121;&#32;&#38; &#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#125;&#125;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#55;&#121;&#125;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#92;&#92;&#32;&#70;&#32;&#38;&#32;&#38;&#32;&#79;&#32;&#38;&#32;&#38;&#32;&#73;&#32;&#38;&#32;&#38;&#32;&#76;&#32;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"216\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 68px\">\n<td style=\"width: 36.9258%;height: 68px\">Multiply the<span style=\"color: #ff0000\"> <em data-effect=\"italics\">Last <\/em><\/span>terms, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-feb273d26ad08d56158041e1749afc8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#45;&#55;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 16.4312%;height: 68px\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_4.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2681\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_4.jpg\" alt=\"This image shows the product of y minus 7 and y plus 4 again, with a fourth arrow extending from minus 7 in the first binomial to 4 in the second binomial.\" width=\"110\" height=\"74\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_4.jpg 120w, https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Ex12_4-65x44.jpg 65w\" sizes=\"auto, (max-width: 110px) 100vw, 110px\" \/><\/a><\/td>\n<td style=\"width: 47.9682%;height: 68px;text-align: center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d12018567da99f74ce330370dd7a2eb2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#121;&#94;&#50;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#52;&#121;&#32;&#38; &#45;&#32;&#38;&#32;&#55;&#121;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#125;&#125;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#50;&#56;&#125;&#125;&#32;&#92;&#92;&#32;&#70;&#32;&#38;&#32;&#38;&#32;&#79;&#32;&#38;&#32;&#38;&#32;&#73;&#32;&#38;&#32;&#38;&#32;&#76;&#32;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"210\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 36.9258%;height: 16px\">Combine like terms.<\/td>\n<td style=\"width: 16.4312%;height: 16px\"><\/td>\n<td style=\"width: 47.9682%;height: 16px;text-align: center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a4bf6f743a17c4b4cff501e2c1125868_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#50;&#45;&#51;&#121;&#45;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596360918\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596360922\" data-type=\"exercise\">\n<div id=\"fs-id1169596360925\" data-type=\"problem\">\n<p id=\"fs-id1169596360927\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-575d477727a560b7902ee31426505f7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596299632\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596299634\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ad6995356298a30c19742b651e98212f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#120;&#45;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"97\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596376719\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596376723\" data-type=\"exercise\">\n<div id=\"fs-id1169596376725\" data-type=\"problem\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596376725\" data-type=\"problem\">\n<p id=\"fs-id1169596557706\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f252a136bf50fd46d2c4aa000fed3d78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596499681\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596499684\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ff7acfa7d24cbdaa7f8cf2464263922e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#98;&#45;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"93\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596376719\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596376723\" data-type=\"exercise\">\n<div id=\"fs-id1169596499681\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596374507\" data-type=\"problem\">\n<p id=\"fs-id1169596374509\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-debed566b4b30d59587a83481aeeb1e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596558267\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-debed566b4b30d59587a83481aeeb1e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%\"><a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Screenshot-2023-06-27-190936.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2676\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Screenshot-2023-06-27-190936.jpg\" alt=\"\" width=\"126\" height=\"77\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Screenshot-2023-06-27-190936.jpg 185w, https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/Screenshot-2023-06-27-190936-65x40.jpg 65w\" sizes=\"auto, (max-width: 126px) 100vw, 126px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Multiply the <em data-effect=\"italics\"><span style=\"color: #ff0000\">First<\/span>\u00a0<\/em>terms, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c489324440e5959daeac87af661785d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#52;&#120;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%\">\n<p style=\"text-align: left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6b2298dbd6f74cbf5760f7f6e129a2ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#56;&#120;&#94;&#50;&#125;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#38; &#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#92;&#92;&#32;&#70;&#32;&#38;&#32;&#38;&#32;&#79;&#32;&#38;&#32;&#38;&#32;&#73;&#32;&#38;&#32;&#38;&#32;&#76;&#32;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"235\" style=\"vertical-align: -11px;\" \/><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Multiply the <em data-effect=\"italics\"><span style=\"color: #ff0000\">Outer<\/span>\u00a0<\/em>terms, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9e3d12885f8017d49677731d8885af97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#52;&#120;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#40;&#45;&#53;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"68\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-abc7d85fc9d9b46d7aa176d80fb81997_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#56;&#120;&#94;&#50;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#125;&#125;&#32;&#38;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#50;&#48;&#120;&#125;&#125;&#32;&#38; &#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#92;&#92;&#32;&#70;&#32;&#38;&#32;&#38;&#32;&#79;&#32;&#38;&#32;&#38;&#32;&#73;&#32;&#38;&#32;&#38;&#32;&#76;&#32;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"240\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Multiply the <span style=\"color: #ff0000\"><em data-effect=\"italics\">Inner <\/em><\/span>terms, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f478c2cef3f670b848fa100692bc8c92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#51;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#120;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7d4caa4b2827848a3550108c76d860e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#56;&#120;&#94;&#50;&#32;&#38;&#32;&#45;&#32;&#38;&#32;&#50;&#48;&#120;&#32;&#38; &#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#43;&#125;&#125;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#54;&#120;&#125;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#92;&#92;&#32;&#70;&#32;&#38;&#32;&#38;&#32;&#79;&#32;&#38;&#32;&#38;&#32;&#73;&#32;&#38;&#32;&#38;&#32;&#76;&#32;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"236\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Multiply the<span style=\"color: #ff0000\"> <em data-effect=\"italics\">Last <\/em><\/span>terms, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-04d966a6ba4e5140b51509768d19c37e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#51;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#40;&#45;&#53;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1d7c35d910c36195a310e886f87f01fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#56;&#120;&#94;&#50;&#32;&#38;&#32;&#45;&#32;&#38;&#50;&#48;&#120;&#32;&#38; &#43;&#32;&#38;&#32;&#54;&#120;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#125;&#125;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#49;&#53;&#125;&#125;&#32;&#92;&#92;&#32;&#70;&#32;&#38;&#32;&#38;&#32;&#79;&#32;&#38;&#32;&#38;&#32;&#73;&#32;&#38;&#32;&#38;&#32;&#76;&#32;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"229\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">Combine like terms.<\/td>\n<td style=\"width: 50%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0227695d71fbf0cf467eb14d3954da2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#94;&#50;&#45;&#49;&#52;&#120;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"115\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596387847\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596455638\" data-type=\"exercise\">\n<div id=\"fs-id1169596455640\" data-type=\"problem\">\n<p id=\"fs-id1169596455642\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0939d17f619afb15365d2ec0086d1ebc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#120;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596310554\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596310556\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2c6507e7fd1bf67631c0d83564c9d42c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#57;&#120;&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"124\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596389245\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596389248\" data-type=\"exercise\">\n<div id=\"fs-id1169596389250\" data-type=\"problem\"><\/div>\n<div id=\"fs-id1169596367182\" data-type=\"solution\">\n<p id=\"fs-id1169596557998\">\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596389250\" data-type=\"problem\">\n<p id=\"fs-id1169596389252\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3099f7429e4df4d8c6ee5859b6b499c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#121;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#121;&#45;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"135\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596367182\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596557998\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-86fea7c9024bb3048f073d5b6d24b829_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#48;&#121;&#45;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"122\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596558024\">The final products in the last four examples were trinomials because we could combine the two middle terms. This is not always the case.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"eip-id1172187806128\" data-type=\"problem\">\n<p id=\"eip-id1172187806130\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-680c08564962689d6148658aafc0967f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#45;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"eip-id1172187806134\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172187806137\" class=\"unnumbered unstyled\" style=\"width: 100%; width: 100%;\" summary=\"This figure has three columns. At the top of the figure, the second column contains the product of two binomials, 3x minus y and 2x minus 5. One row down, the text in the first column says \u201cMultiply the first terms.\u201d The second column contains 6x squared plus blank plus blank plus blank. Beneath 6x squared is the letter F and beneath each blank are the letters O, I, and L, respectively. One row down, the text in the first column says \u201cMultiply the outer terms.\u201d The second column contains 6x squared minus 15x plus blank plus blank. Below 6x squared is F, below 15x is O, and below the blanks are I and L. One row down, the text in the first column says \u201cMultiply the inner terms.\u201d The second column contains 6x squared minus 15x minus 2xy plus blank. One row down, the text in the first column says \u201cMultiply the last terms.\u201d The second column contains the full expression, 6x squared minus 15x minus 2xy plus 5y, with each letter of FOIL beneath each of the terms. At the bottom of the image, the text in the first column says \u201cCombine like terms\u2014there are none.\u201d In the right column is 6x squared minus 15x minus 2xy plus 5y. In the third column is the product of the two binomials again, 3x minus y times 2x minus 5. An arrow extends from 3x in the first binomial to 2x in the second binomial. A second arrow extends from 3x in the first binomial to minus 5 in the second binomial. A third arrow extends from y in the first binomial to 2x in the second binomial. A fourth arrow extends from y in the first binomial to minus 5 in the second binomial.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 44.0812%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-680c08564962689d6148658aafc0967f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#45;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 55.8304%\"><span id=\"eip-id1172187806172\" data-type=\"media\" data-alt=\"An arrow extends from 3 x in the first binomial to 2 x in the second binomial. A second arrow extends from 3 x in the first binomial to minus 5 in the second binomial. A third arrow extends from y in the first binomial to 2 x in the second binomial. A fourth arrow extends from y in the first binomial to minus 5 in the second binomial.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_018b_img_new.jpg\" alt=\"An arrow extends from 3 x in the first binomial to 2 x in the second binomial. A second arrow extends from 3 x in the first binomial to minus 5 in the second binomial. A third arrow extends from y in the first binomial to 2 x in the second binomial. A fourth arrow extends from y in the first binomial to minus 5 in the second binomial.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 44.0812%\">Multiply the <em data-effect=\"italics\">First<\/em>.<\/td>\n<td style=\"width: 55.8304%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-300c967454ccf9865432832ce9da3444_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#54;&#120;&#94;&#50;&#125;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#38;&#43;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#92;&#92;&#32;&#70;&#38;&#38;&#79;&#38;&#38;&#73;&#38;&#38;&#76;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"235\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 44.0812%\">Multiply the <em data-effect=\"italics\">Outer<\/em>.<\/td>\n<td style=\"width: 55.8304%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-86c644d1d7f92e5047fc10f3c59ccc0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#54;&#120;&#94;&#50;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#125;&#125;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#49;&#53;&#120;&#125;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#38;&#43;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#92;&#92;&#32;&#70;&#38;&#38;&#79;&#38;&#38;&#73;&#38;&#38;&#76;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"240\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 44.0812%\">Multiply the <em data-effect=\"italics\">Inner<\/em>.<\/td>\n<td style=\"width: 55.8304%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fd07cfe2e68ab3e24dc739d03665f2f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#54;&#120;&#94;&#50;&#32;&#38;&#32;&#45;&#32;&#38;&#32;&#49;&#53;&#120;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#125;&#125;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#50;&#120;&#121;&#125;&#125;&#32;&#38;&#43;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#92;&#92;&#32;&#70;&#38;&#38;&#79;&#38;&#38;&#73;&#38;&#38;&#76;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"245\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 44.0812%\">Multiply the <em data-effect=\"italics\">Last<\/em>.<\/td>\n<td style=\"width: 55.8304%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fea124768950cc8ed45ac14157acc566_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#54;&#120;&#94;&#50;&#32;&#38;&#32;&#45;&#32;&#38;&#32;&#49;&#53;&#120;&#32;&#38;&#32;&#45;&#32;&#38;&#32;&#50;&#120;&#121;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#43;&#125;&#125;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#53;&#121;&#125;&#125;&#32;&#92;&#92;&#32;&#70;&#38;&#38;&#79;&#38;&#38;&#73;&#38;&#38;&#76;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"239\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 44.0812%\">Combine like terms\u2014there are none.<\/td>\n<td style=\"width: 55.8304%\"><span id=\"eip-id1172187828927\" data-type=\"media\" data-alt=\"6 x squared minus 15 x minus 2 x y plus 5 y.\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-baf4fc62e2a83d57a4a6a90551c48595_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#32;&#120;&#94;&#50;&#45;&#49;&#53;&#32;&#120;&#45;&#50;&#32;&#120;&#32;&#121;&#43;&#53;&#32;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"166\" style=\"vertical-align: -4px;\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596365886\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596365861\" data-type=\"exercise\">\n<div id=\"fs-id1169596365863\" data-type=\"problem\">\n<p id=\"fs-id1169596365865\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-47c073219eb0598d0dfd3a939339af5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#99;&#45;&#100;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#99;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"123\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596555914\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596555916\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f215c966238a9178a9aaf1ef804f25dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#48;&#99;&#45;&#99;&#100;&#43;&#54;&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"158\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596557849\" data-type=\"problem\">\n<p id=\"fs-id1169596557851\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c35a84b5c89912a810ee37d033d5c022_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#120;&#45;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596439984\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596439987\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e134d9bf57e7c10e32f535e7b7236570_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#53;&#120;&#45;&#50;&#120;&#121;&#43;&#53;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"174\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596396823\">Be careful of the exponents in the next example.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596452002\" data-type=\"problem\">\n<p id=\"fs-id1169596452004\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d24068f5b7e9db588f5d983da33cab47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"120\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1172187963608\" class=\"unnumbered unstyled\" summary=\"This figure has three columns. At the top of the figure, the second column contains the product of two binomials, n squared plus 4 and n minus 1. One row down, the text in the first column says \u201cMultiply the first terms.\u201d The second column contains n cubed plus blank plus blank plus blank. Beneath n cubed is the letter F and beneath each blank are the letters O, I, and L, respectively. One row down, the text in the first column says \u201cMultiply the outer terms.\u201d The second column contains n cubed minus n squared plus blank plus blank. Below n cubed is F, below n squared is O, and below the blanks are I and L. One row down, the text in the first column says \u201cMultiply the inner terms.\u201d The second column contains n cubed minus n squared plus 4n plus blank. One row down, the text in the first column says \u201cMultiply the last terms.\u201d The second column contains the full expression, n cubed minus n squared plus 4n minus 4, with each letter of FOIL beneath each of the terms. At the bottom of the image, the text in the first column says \u201cCombine like terms\u2014there are none.\u201d In the right column is n cubed minus n squared plus 4n minus 4. In the third column is the product of the two binomials again, n squared plus 4 times n minus 1. An arrow extends from n cubed in the first binomial to n in the second binomial. A second arrow extends from n cubed in the first binomial to minus 1 in the second binomial. A third arrow extends from 4 in the first binomial to n in the second binomial. A fourth arrow extends from 4 in the first binomial to minus 1 in the second binomial.\" data-label=\"\">\n<tbody>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d24068f5b7e9db588f5d983da33cab47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"120\" style=\"vertical-align: -7px;\" \/><\/td>\n<td><span id=\"eip-id1172187963665\" data-type=\"media\" data-alt=\"The product of two binomials, n squared plus 4 and n minus 1. An arrow extends from n squared in the first binomial to n in the second binomial. A second arrow extends from n squared in the first binomial to minus 1 in the second binomial. A third arrow extends from 4 in the first binomial to n in the second binomial. A fourth arrow extends from 4 in the first binomial to minus 1 in the second binomial.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_019b_img_new.jpg\" alt=\"The product of two binomials, n squared plus 4 and n minus 1. An arrow extends from n squared in the first binomial to n in the second binomial. A second arrow extends from n squared in the first binomial to minus 1 in the second binomial. A third arrow extends from 4 in the first binomial to n in the second binomial. A fourth arrow extends from 4 in the first binomial to minus 1 in the second binomial.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply the <em data-effect=\"italics\">First<\/em>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f77a00062da0f170611f7c0520253b47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#110;&#94;&#51;&#125;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#38;&#43;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#92;&#92;&#32;&#70;&#38;&#38;&#79;&#38;&#38;&#73;&#38;&#38;&#76;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"227\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply the <em data-effect=\"italics\">Outer<\/em>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1a71c7d9f1ee2191512d4f18ee7aa850_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#110;&#94;&#51;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#125;&#125;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#110;&#94;&#50;&#125;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#38;&#43;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#92;&#92;&#32;&#70;&#38;&#38;&#79;&#38;&#38;&#73;&#38;&#38;&#76;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"222\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply the <em data-effect=\"italics\">Inner<\/em>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ffafe9ba02ea879f208f95186e761aa9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#110;&#94;&#51;&#32;&#38;&#32;&#45;&#32;&#38;&#32;&#110;&#94;&#50;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#52;&#110;&#125;&#125;&#32;&#38;&#43;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#92;&#92;&#32;&#70;&#38;&#38;&#79;&#38;&#38;&#73;&#38;&#38;&#76;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"219\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply the <em data-effect=\"italics\">Last<\/em>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f9123d36f3693ed7ab134ffa796339ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#110;&#94;&#51;&#32;&#38;&#32;&#45;&#32;&#38;&#32;&#110;&#94;&#50;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#52;&#110;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#125;&#125;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#52;&#125;&#125;&#32;&#92;&#92;&#32;&#70;&#38;&#38;&#79;&#38;&#38;&#73;&#38;&#38;&#76;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"207\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms\u2014there are none.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ff7cf5f8c46a0574a99a1ca168fdc014_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#94;&#51;&#45;&#110;&#94;&#50;&#43;&#52;&#32;&#110;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"130\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596258587\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596258591\" data-type=\"exercise\">\n<div id=\"fs-id1169596258593\" data-type=\"problem\">\n<p id=\"fs-id1169596555098\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-31218a31198701e73c81c74ea73fadeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"119\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596499635\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596499638\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-28cd8895003059256644ee2aa20bf1da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#56;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#120;&#45;&#52;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"147\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596557426\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596557429\" data-type=\"exercise\">\n<div id=\"fs-id1169596557431\" data-type=\"problem\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596557431\" data-type=\"problem\">\n<p id=\"fs-id1169596557433\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6c738013cc52fb1056997a9eb443688a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"118\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596499357\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596499359\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4392450aedd69d840c8eead660608595_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#45;&#57;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#121;&#45;&#54;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"144\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596258587\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596258591\" data-type=\"exercise\">\n<div id=\"fs-id1169596258593\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596371201\" data-type=\"problem\">\n<p id=\"fs-id1169596371203\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3ce6be347a387739ae295f7ba587cbcc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#112;&#113;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#112;&#113;&#45;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"152\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596366996\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172187720059\" class=\"unnumbered unstyled\" style=\"height: 189px;width: 100%\" summary=\"This figure has three columns. At the top of the figure, the second column contains the product of two binomials, 3pq plus 5 and 6pq minus 11. One row down, the text in the first column says \u201cMultiply the first terms.\u201d The second column contains 18p squared q squared plus blank plus blank plus blank. Beneath 18p squared q squared is the letter F and beneath each blank are the letters O, I, and L, respectively. One row down, the text in the first column says \u201cMultiply the outer terms.\u201d The second column contains 18p squared q squared minus 33pq plus blank plus blank. Below 18p squared q squared is F, below 33pq is O, and below the blanks are I and L. One row down, the text in the first column says \u201cMultiply the inner terms.\u201d The second column contains 18p squared q squared minus 33pq plus 30pq plus blank. One row down, the text in the first column says \u201cMultiply the last terms.\u201d The second column contains the full expression, 18p squared q squared minus 33pq plus 30pq minus 55, with each letter of FOIL beneath each of the terms. At the bottom of the image, the text in the first column says \u201cCombine like terms.\u201d In the right column is 18p squared q squared minus 3pq minus 55. In the third column is the product of the two binomials again, 3pq plus 5 times 6pq minus 11. An arrow extends from 3pq in the first binomial to 6pq in the second binomial. A second arrow extends from 3pq in the first binomial to minus 11 in the second binomial. A third arrow extends from 5 in the first binomial to 6pq in the second binomial. A fourth arrow extends from 5 in the first binomial to minus 11 in the second binomial.\" data-label=\"\">\n<tbody>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7d2a7e0dbb6e3d8ebb31aa895c253af0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#51;&#112;&#113;&#43;&#53;&#41;&#40;&#54;&#112;&#113;&#45;&#49;&#49;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\" \/><\/td>\n<td><span id=\"eip-id1172187720114\" data-type=\"media\" data-alt=\"The product of two binomials, 3 p q plus 5 and 6 p q minus 11. An arrow extends from 3 p q in the first binomial to 6 p q in the second binomial. A second arrow extends from 3 p q in the first binomial to minus 11 in the second binomial. A third arrow extends from 5 in the first binomial to 6 p q in the second binomial. A fourth arrow extends from 5 in the first binomial to minus 11 in the second binomial.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_020b_img_new.jpg\" alt=\"The product of two binomials, 3 p q plus 5 and 6 p q minus 11. An arrow extends from 3 p q in the first binomial to 6 p q in the second binomial. A second arrow extends from 3 p q in the first binomial to minus 11 in the second binomial. A third arrow extends from 5 in the first binomial to 6 p q in the second binomial. A fourth arrow extends from 5 in the first binomial to minus 11 in the second binomial.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply the <em data-effect=\"italics\">First<\/em>.<\/td>\n<td>\n<p style=\"text-align: left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-712657c9ee7436361b020881c294c442_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#49;&#56;&#112;&#94;&#50;&#113;&#94;&#50;&#125;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#38; &#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#92;&#92;&#32;&#70;&#32;&#38;&#32;&#38;&#32;&#79;&#32;&#38;&#32;&#38;&#32;&#73;&#32;&#38;&#32;&#38;&#32;&#76;&#32;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"258\" style=\"vertical-align: -11px;\" \/><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>Multiply the <em data-effect=\"italics\">Outer<\/em>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-47a844a3c940df5e250a3683dfe599b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#49;&#56;&#112;&#94;&#50;&#113;&#94;&#50;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#125;&#125;&#32;&#38;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#51;&#51;&#112;&#113;&#125;&#125;&#32;&#38; &#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#92;&#92;&#32;&#70;&#32;&#38;&#32;&#38;&#32;&#79;&#32;&#38;&#32;&#38;&#32;&#73;&#32;&#38;&#32;&#38;&#32;&#76;&#32;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"270\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply the <em data-effect=\"italics\">Inner<\/em>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-beb7cae51384df10018153c6ed78179b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#49;&#56;&#112;&#94;&#50;&#113;&#94;&#50;&#32;&#38;&#32;&#45;&#32;&#38;&#51;&#51;&#112;&#113;&#32;&#38; &#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#43;&#125;&#125;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#51;&#48;&#112;&#113;&#125;&#125;&#32;&#38;&#32;&#43;&#32;&#38;&#32;&#92;&#114;&#117;&#108;&#101;&#123;&#46;&#53;&#99;&#109;&#125;&#123;&#48;&#46;&#52;&#112;&#116;&#125;&#32;&#92;&#92;&#32;&#70;&#32;&#38;&#32;&#38;&#32;&#79;&#32;&#38;&#32;&#38;&#32;&#73;&#32;&#38;&#32;&#38;&#32;&#76;&#32;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"283\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply the <em data-effect=\"italics\">Last<\/em>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-752402813ac0c14fe88333531b3a029c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#32;&#49;&#56;&#112;&#94;&#50;&#113;&#94;&#50;&#32;&#38;&#32;&#45;&#32;&#38;&#51;&#51;&#112;&#113;&#32;&#38; &#43;&#32;&#38;&#32;&#51;&#48;&#112;&#113;&#32;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#125;&#125;&#38;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#53;&#53;&#125;&#125;&#32;&#92;&#92;&#32;&#70;&#32;&#38;&#32;&#38;&#32;&#79;&#32;&#38;&#32;&#38;&#32;&#73;&#32;&#38;&#32;&#38;&#32;&#76;&#32;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"276\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d37c9cd49613db0a7db0debd53589498_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#32;&#112;&#94;&#50;&#32;&#113;&#94;&#50;&#45;&#51;&#32;&#112;&#32;&#113;&#45;&#53;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596557426\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596557429\" data-type=\"exercise\">\n<div id=\"fs-id1169596499357\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596555522\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596555526\" data-type=\"exercise\">\n<div id=\"fs-id1169596555528\" data-type=\"problem\">\n<p id=\"fs-id1169596555530\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2bc01b03535927800be7e654797eeb0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#97;&#98;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#97;&#98;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596557487\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596384829\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a4b490496ae0ce0929277e84e2473513_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#97;&#98;&#45;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"137\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596384862\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596384865\" data-type=\"exercise\">\n<div id=\"fs-id1169596556552\" data-type=\"problem\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596556552\" data-type=\"problem\">\n<p id=\"fs-id1169596556554\">Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8add0a24529da5bb0d06421358e7065b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#121;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#120;&#121;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596296045\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596296047\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8ae5d7022b628de92e7d13f83e8e3c4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#120;&#121;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"132\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Multiply a Binomial by a Binomial Using the Vertical Method<\/h1>\n<p id=\"fs-id1169596303991\">The FOIL method is usually the quickest method for multiplying two binomials, but it <em data-effect=\"italics\">only<\/em> works for binomials. You can use the Distributive Property to find the product of any two polynomials. Another method that works for all polynomials is the Vertical Method. It is very much like the method you use to multiply whole numbers. Look carefully at this example of multiplying two-digit numbers.<\/p>\n<p><span id=\"fs-id1169596304009\" data-type=\"media\" data-alt=\"This figure shows the vertical multiplication of 23 and 46. The number 23 is above the number 46. Below this, there is the partial product 138 over the partial product 92. The final product is at the bottom and is 1058. Text on the right side of the image says \u201cStart by multiplying 23 by 6 to get 138. Next, multiply 23 by 4, lining up the partial product in the correct columns. Last you add the partial products.\u201d\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_021_img_new.jpg\" alt=\"This figure shows the vertical multiplication of 23 and 46. The number 23 is above the number 46. Below this, there is the partial product 138 over the partial product 92. The final product is at the bottom and is 1058. Text on the right side of the image says \u201cStart by multiplying 23 by 6 to get 138. Next, multiply 23 by 4, lining up the partial product in the correct columns. Last you add the partial products.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596304017\">Now we\u2019ll apply this same method to multiply two binomials.<\/p>\n<div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 17<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"textbox__content\">\n<p>Multiply using the Vertical Method: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5d7216a42060890b6b1a5b8aef053299_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#121;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#121;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>It does not matter which binomial goes on the top.<\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 30.6922%\">Setup for Vertical multiplication<\/td>\n<td style=\"text-align: right;width: 35.7013%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7dad239336fe540222c83a58e1d4a996_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#114;&#125;&#32;&#51;&#121;&#45;&#49;&#32;&#92;&#92;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#98;&#108;&#117;&#101;&#125;&#123;&#32;&#50;&#121;&#125;&#125;&#45;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#54;&#125;&#125;&#32;&#92;&#92;&#32;&#92;&#104;&#108;&#105;&#110;&#101;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"97\" style=\"vertical-align: -18px;\" \/><\/td>\n<td style=\"width: 33.5155%\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 30.6922%\">Multiply <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e5654448e264ba9825b53f58fe0d7e4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#121;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"48\" style=\"vertical-align: -4px;\" \/> by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9cdf435c5a208b49f5981b4859a8eb89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#32;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><br \/>\nMultiple <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e5654448e264ba9825b53f58fe0d7e4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#121;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"48\" style=\"vertical-align: -4px;\" \/> by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c5e7f12bbe539ec43f75cf9a765f74db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#98;&#108;&#117;&#101;&#125;&#32;&#50;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"18\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"text-align: right;width: 35.7013%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-91343d58908eb0f6e7d27cd45fbaf3d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#114;&#125;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#49;&#56;&#121;&#43;&#54;&#125;&#125;&#32;&#92;&#92;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#98;&#108;&#117;&#101;&#125;&#123;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#32;&#45;&#50;&#121;&#125;&#125;&#32;&#92;&#104;&#115;&#112;&#97;&#99;&#101;&#123;&#48;&#46;&#57;&#99;&#109;&#125;&#32;&#92;&#92;&#32;&#92;&#104;&#108;&#105;&#110;&#101;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"88\" style=\"vertical-align: -18px;\" \/><\/td>\n<td style=\"width: 33.5155%\">Partial Product <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-02f087545ac492f8a878c5787c0da731_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#56;&#121;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"71\" style=\"vertical-align: -4px;\" \/><br \/>\nPartial Product <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8797e7198720ee222d59bea6736f4b8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#32;&#45;&#50;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 30.6922%\">Add like terms.<\/td>\n<td style=\"text-align: right;width: 35.7013%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f29de0ae00a0a319d3c17f06db1863bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#121;&#94;&#50;&#32;&#92;&#104;&#115;&#112;&#97;&#99;&#101;&#123;&#48;&#46;&#50;&#99;&#109;&#125;&#32;&#45;&#50;&#48;&#32;&#121;&#32;&#92;&#104;&#115;&#112;&#97;&#99;&#101;&#123;&#48;&#46;&#50;&#99;&#109;&#125;&#32;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.5155%\">Product <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f803ced7200aba90c0ad9a5470b043dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#32;&#45;&#32;&#50;&#48;&#121;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>If you use the FOIL method to multiply these binomials you will notice that the partial products are the same as the terms in the FOIL method.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596556869\">Multiply using the Vertical Method: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e862e0a186964dde6ae5fad0cfd3fb1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#109;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#109;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"139\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596556869\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4a0c74daf2826264b55547764ea413f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#49;&#109;&#43;&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"134\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596556861\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596556861\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596556864\" data-type=\"exercise\">\n<div id=\"fs-id1169596556864\" data-type=\"exercise\">\n<div id=\"fs-id1169596497567\" data-type=\"solution\">\n<div id=\"fs-id1169596497567\" data-type=\"solution\">\n<p id=\"fs-id1169596497570\">Multiply using the Vertical Method: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5f379df422a25f3462f58b102fcfa6da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#98;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#98;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"123\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596497595\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596497595\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596497599\" data-type=\"exercise\">\n<div id=\"fs-id1169596497599\" data-type=\"exercise\">\n<div id=\"fs-id1169596497601\" data-type=\"problem\">\n<div id=\"fs-id1169596497601\" data-type=\"problem\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596499276\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3515bbe8cd8a33d03ab1298f766b8bff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#50;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#51;&#98;&#43;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"119\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596499713\">We have now used three methods for multiplying binomials. Be sure to practice each method, and try to decide which one you prefer. The methods are listed here all together, to help you remember them.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Multiplying Two Binomials<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>To multiply binomials, use the:<\/p>\n<ul>\n<li style=\"list-style-type: none\">\n<ul id=\"fs-id1169596499726\" data-bullet-style=\"bullet\">\n<li>Distributive Property<\/li>\n<li>FOIL Method<\/li>\n<li>Vertical Method<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596499718\" data-type=\"note\">\n<div id=\"fs-id1169596499718\" data-type=\"note\">\n<p id=\"fs-id1171792350534\">Remember, FOIL only works when multiplying two binomials.<\/p>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Multiply a Trinomial by a Binomial<\/h1>\n<p id=\"fs-id1169596410089\">We have multiplied monomials by monomials, monomials by polynomials, and binomials by binomials. Now we\u2019re ready to multiply a <span class=\"no-emphasis\" data-type=\"term\">trinomial<\/span> by a <span class=\"no-emphasis\" data-type=\"term\">binomial<\/span>. Remember, FOIL will not work in this case, but we can use either the Distributive Property or the Vertical Method. We first look at an example using the Distributive Property.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 18<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596410109\" data-type=\"problem\">\n<p id=\"fs-id1169596410111\">Multiply using the Distributive Property: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9352aafbcd986f55ab16ec300fec0287_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#98;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"161\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596558245\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172187617554\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. In the first row, the right column contains the product of a binomial, b plus 3, and a trinomial, 2b squared minus 5b plus 8. Two red arrows extend from the trinomial, terminating at b and 3 in the binomial. In the second row, the text in the left column says \u201cDistribute.\u201d In the right column is b times 2b squared minus 5b plus 8 plus 3 times 2b squared minus 5b plus 8, where 2b squared minus 5b plus 8 is in parentheses twice. In the third row, the text in the left column says \u201cMultiply.\u201d In the right column is 2b cubed minus 5b squared plus 8b plus 6b squared minus 15b plus 24. In the last row, the text in the left column says \u201cCombine like terms.\u201d In the right column is 2b cubed plus b squared minus 7b plus 24.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187617574\" data-type=\"media\" data-alt=\"The product of a binomial, b plus 3, and a trinomial, 2 b squared minus 5 b plus 8. Two arrows extend from the trinomial, terminating at b and 3 in the binomial.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_024a_img_new.jpg\" alt=\"The product of a binomial, b plus 3, and a trinomial, 2 b squared minus 5 b plus 8. Two arrows extend from the trinomial, terminating at b and 3 in the binomial.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1172187617591\" data-type=\"media\" data-alt=\"The sum of two products, the product of b and 2 b squared minus 5 b plus 8, and the product of 3 and 2 b squared minus 5 b plus 8.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/06\/CNX_ElemAlg_Figure_06_03_024b_img_new.jpg\" alt=\"The sum of two products, the product of b and 2 b squared minus 5 b plus 8, and the product of 3 and 2 b squared minus 5 b plus 8.\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-38657545cc45726c012e2da94c3a8eff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#32;&#98;&#94;&#51;&#45;&#53;&#98;&#94;&#50;&#43;&#56;&#98;&#43;&#54;&#98;&#94;&#50;&#45;&#49;&#53;&#32;&#98;&#43;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"241\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1172187617625\" data-type=\"media\" data-alt=\"2 b cubed plus b squared minus 7 b plus 24.\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c63576a474ddc8ac07894cd7d29c7751_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#32;&#98;&#94;&#51;&#43;&#98;&#94;&#50;&#45;&#55;&#32;&#98;&#43;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"139\" style=\"vertical-align: -2px;\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 18.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596369771\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596369775\" data-type=\"exercise\">\n<div id=\"fs-id1169596369777\" data-type=\"problem\">\n<p id=\"fs-id1169596369779\">Multiply using the Distributive Property: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c0e0837c179c91509101dd38f685b5c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#121;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"157\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<div data-type=\"solution\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-07184f6185b9c44eb5958771df6e2091_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#45;&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#55;&#121;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"144\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 18.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596348894\" data-type=\"problem\">\n<p id=\"fs-id1169596348896\">Multiply using the Distributive Property: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-df2b7a82b5db13f119030ecc1431156e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"169\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596555021\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596555023\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-60ebe7e4f33e408e1a5339003d0f8a6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#43;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#120;&#43;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"155\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596498300\">Now let\u2019s do this same multiplication using the Vertical Method.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 19<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596498309\" data-type=\"problem\">\n<p id=\"fs-id1169596498311\">Multiply using the Vertical Method: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9352aafbcd986f55ab16ec300fec0287_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#98;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"161\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596554965\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596554970\">It is easier to put the polynomial with fewer terms on the bottom because we get fewer partial products this way.<\/p>\n<table id=\"eip-id1172187963535\" class=\"unnumbered unstyled\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure, the right column contains the vertical multiplication of 2b squared minus 5b plus 8 and b plus 3. The text in the left column says \u201cMultiply 2b squared minus 5b plus 8 by 3.\u201d In the right column is the partial product 6b squared minus 15b plus 24. One line down, the text in the left column says \u201cMultiply 2b squared minus 5b plus 8 by b.\u201d In the right column is the partial product 2b cubed minus 5b squared plus 8b. One line down, the text in the left column says \u201cAdd like terms.\u201d In the right column is the fully expanded expression: 2b cubed plus b squared minus 7b plus 24.\" data-label=\"\">\n<tbody>\n<tr>\n<td data-valign=\"bottom\">Rewrite the question in vertical setup<\/td>\n<td style=\"text-align: right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dad0cf64ac09dd603488f0d411cb78db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#114;&#125;&#32;&#50;&#32;&#98;&#94;&#50;&#45;&#53;&#32;&#98;&#43;&#56;&#32;&#92;&#92;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#98;&#108;&#117;&#101;&#125;&#123;&#32;&#98;&#125;&#125;&#43;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#51;&#125;&#125;&#32;&#92;&#92;&#32;&#92;&#104;&#108;&#105;&#110;&#101;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"110\" style=\"vertical-align: -18px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply (2<em data-effect=\"italics\">b<\/em><sup>2<\/sup> \u2212 5<em data-effect=\"italics\">b<\/em> + 8) by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c13dcbd2954acf05d2fa64fc997bbd78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<br \/>\nMultiply (2<em data-effect=\"italics\">b<\/em><sup>2<\/sup> \u2212 5<em data-effect=\"italics\">b<\/em> + 8) by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-74282124552136c04f5b9d86177f9984_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#98;&#108;&#117;&#101;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"text-align: right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dd84ba7dfed713f1f374374c3ef5d952_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#114;&#125;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#54;&#32;&#98;&#94;&#50;&#45;&#49;&#53;&#32;&#98;&#43;&#50;&#52;&#125;&#125;&#32;&#92;&#92;&#32;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#98;&#108;&#117;&#101;&#125;&#123;&#50;&#98;&#94;&#51;&#45;&#53;&#98;&#94;&#50;&#43;&#56;&#98;&#125;&#125;&#32;&#92;&#104;&#115;&#112;&#97;&#99;&#101;&#123;&#48;&#46;&#57;&#99;&#109;&#125;&#32;&#92;&#92;&#32;&#92;&#104;&#108;&#105;&#110;&#101;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"127\" style=\"vertical-align: -18px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add like terms.<\/td>\n<td style=\"text-align: right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-48db8bb3bc9adc7207aaef4332cb316c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#32;&#98;&#94;&#51;&#32;&#32;&#43;&#98;&#94;&#50;&#32;&#92;&#104;&#115;&#112;&#97;&#99;&#101;&#123;&#48;&#46;&#50;&#99;&#109;&#125;&#32;&#45;&#55;&#32;&#98;&#32;&#92;&#104;&#115;&#112;&#97;&#99;&#101;&#123;&#48;&#46;&#50;&#99;&#109;&#125;&#32;&#43;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"157\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>There are no more like terms that can be collected.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c63576a474ddc8ac07894cd7d29c7751_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#32;&#98;&#94;&#51;&#43;&#98;&#94;&#50;&#45;&#55;&#32;&#98;&#43;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"139\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 19.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596382893\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596382897\" data-type=\"exercise\">\n<div id=\"fs-id1169596382899\" data-type=\"problem\">\n<p id=\"fs-id1169596382901\">Multiply using the Vertical Method: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c0e0837c179c91509101dd38f685b5c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#121;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"157\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596555484\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596555486\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-07184f6185b9c44eb5958771df6e2091_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#45;&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#55;&#121;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"144\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 19.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596557069\" data-type=\"problem\">\n<p id=\"fs-id1169596557071\">Multiply using the Vertical Method: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-df2b7a82b5db13f119030ecc1431156e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"169\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596559250\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596559252\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-60ebe7e4f33e408e1a5339003d0f8a6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#43;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#120;&#43;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"155\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596559287\">We have now seen two methods you can use to multiply a <span class=\"no-emphasis\" data-type=\"term\">trinomial<\/span> by a binomial. After you practice each method, you\u2019ll probably find you prefer one way over the other. We list both methods are listed here, for easy reference.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Multiply a Trinomial by a Binomial<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596559298\">To multiply a trinomial by a binomial, use the:<\/p>\n<ul id=\"fs-id1169596291508\" data-bullet-style=\"bullet\">\n<li>Distributive Property<\/li>\n<li>Vertical Method<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596559293\" data-type=\"note\">\n<div data-type=\"title\">\n<p>Access these online resources for additional instruction and practice with multiplying polynomials:<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596291522\" class=\"media-2\" data-type=\"note\">\n<ul id=\"fs-id1169596291531\" data-display=\"block\">\n<li><a href=\"https:\/\/openstax.org\/l\/25MultiplyExp1\">Multiplying Exponents 1<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/25MultiplyExp2\">Multiplying Exponents 2<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/25MultiplyExp3\">Multiplying Exponents 3<\/a><\/li>\n<\/ul>\n<\/div>\n<h1 data-type=\"title\">Key Concepts<\/h1>\n<ul id=\"fs-id1169596457026\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">FOIL Method for Multiplying Two Binomials<\/strong>\u2014To multiply two binomials:\n<ol id=\"fs-id1168741741690\" class=\"stepwise\" type=\"1\">\n<li>Multiply the <strong data-effect=\"bold\">First<\/strong> terms.<\/li>\n<li>Multiply the <strong data-effect=\"bold\">Outer<\/strong> terms.<\/li>\n<li>Multiply the <strong data-effect=\"bold\">Inner<\/strong> terms.<\/li>\n<li>Multiply the <strong data-effect=\"bold\">Last<\/strong> terms.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Multiplying Two Binomials<\/strong>\u2014To multiply binomials, use the:\n<ul id=\"fs-id1169596557780\" data-bullet-style=\"open-circle\">\n<li>Distributive Property (<a class=\"autogenerated-content\" href=\"#fs-id1169596308817\">(Figure)<\/a>)<\/li>\n<li>FOIL Method (<a class=\"autogenerated-content\" href=\"#fs-id1169596450766\">(Figure)<\/a>)<\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Multiplying a Trinomial by a Binomial<\/strong>\u2014To multiply a trinomial by a binomial, use the:\n<ul id=\"fs-id1169596557816\" data-bullet-style=\"open-circle\">\n<li>Distributive Property (<a class=\"autogenerated-content\" href=\"#fs-id1169596410105\">(Figure)<\/a>)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h1 style=\"text-align: left\" data-type=\"title\">Practice Makes Perfect<\/h1>\n<h2 style=\"text-align: left\" data-type=\"title\">Multiply a Polynomial by a Monomial<\/h2>\n<p id=\"fs-id1168745407238\">In the following exercises, multiply.<\/p>\n<table style=\"border-collapse: collapse;width: 100%;height: 476px\">\n<tbody>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">1. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-30de6e061d0f1a1ef1cca15d85cae52a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#119;&#43;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">2. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bdd2ab4682f7ffb8d6d0efa0ead8873c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"63\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1435d88d4a19e5a58467b4b2968a9bd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">4. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ffe70fe3d5c9a7ee14805a28b8c41624_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-929f1faf4143bc720592c1ad64208b44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">6. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a3c226bac0cc4234f2acaa945aa9dbd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ac93afdb370b3d16db5edd162308adba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#107;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">8. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4ca30ea605d3ca0e6d48273f39351dba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#106;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0bc12a18435c79e252af1f8f2a65269b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"64\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">10. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ff09cc6be99813e7bcad1870e53adcbd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#92;&#108;&#101;&#102;&#116;&#40;&#107;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5ceddb37c4e0977bb50b73e1d40bdbc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#98;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0ec4461821c96ac71ae999e6f683ae14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#121;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-480e0c79971e89f9403cd714acfdf380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"89\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">14. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0f3a0f13df1fa797807ff1abc8a59cc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#112;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5cd78d823795ebcbf1de55576c7c9ce3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#114;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#114;&#43;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"80\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">16. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-27deacfd141cc67e5ad2ed9eb8b1b641_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#99;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#99;&#43;&#100;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"80\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-92d47caefff88ac2a1254c6ec2de1768_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">18. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7a3c51657ed8a4fda7a4a57f62885a23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-91e67f73c3a097c8730a0e46f12d5519_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#97;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cb42f27883db126f19796919bc68cd24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#112;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#112;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"95\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9ed9d4e954c2eade4ba20f95cc950fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#48;&#112;&#43;&#50;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"131\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-523f53f17670b4e3b7734b101290f92f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#56;&#121;&#43;&#49;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"122\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-70398110e04a0599419f3323304f4bc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#120;&#45;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"147\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-20cc4203bca2e9d6d901da60960a03b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#116;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#116;&#45;&#49;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"136\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9e3627f60c7636c81d8687bf1bdb62a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#45;&#50;&#113;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"128\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f25cf2329971a6b433eef228769e4a36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#45;&#51;&#120;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"133\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f897468ddc6eadfb573fbd4e4f177a3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#121;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#121;&#45;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"145\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-21645e5a18435dbcf5745181b35396eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#109;&#45;&#49;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"163\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8a2b23ba902af2a61a64cc5cb6ccb53e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#113;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"128\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ae0309e565aea5eb855df6089dec8e5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#123;&#114;&#125;&#94;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#114;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"128\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9762d9fa6c730e676b2bb1b05938e6d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#122;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"160\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">32. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9e9d1a4a17837b91e44950ccd1c57a86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#48;&#120;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"163\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4947129a86c219301974b1b1368b5b71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#109;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">34. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-05fe97702758bb4272c783a2e93e9d63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#106;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#106;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"71\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-480bcd8168a2e73756a84e52412ecfdb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#119;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#32;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">36. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e5c2c74c5dc5d41fbb1ae98d5951542e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#107;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e15995d569c8b0a312ef14b4e809bbb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e3999131174588e2ea39c73254d84186_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3bfd2e0c27a911365ed988f90df1358e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#45;&#50;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"81\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">40. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e9c38459c82054ad2653acf80ae47f10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#118;&#45;&#51;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"81\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d362836ff1c87ac058dd62013c2d6658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">42. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2f789ecb159c0b4399b6ca8c5d8cd47e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a963a5aa0ab09322ce7e9db5a8833ecf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">44. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-05fc864aef01b8c44e1cc5049c574a5e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f33766183e155a2f923ce79c5b93b25b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#117;&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"67\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">46. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-025e73353bcb9e39b20bda9e471629f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"64\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5041fe2528df2a1c690d430cae1f1ef4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"88\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">48. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-40125b472a0cd472e73b1b88a08eb4fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"80\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bcc64b604e0501b312fdf13cf1db3f26_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#120;&#43;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">50. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bb1f669f6e347601905f2cc123ebe24a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#97;&#43;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c8138a52ff460b7da201d2eb5fe64d09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#112;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#49;&#112;&#45;&#53;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"99\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">52. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dd745dafb7742cde0041dd7739235875_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#117;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#117;&#45;&#52;&#118;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-77f120d260f6e55704dd090405da295d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#48;&#118;&#43;&#50;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"131\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">54. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5ec4548b44ceacb4780edb8640e3ff51_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#56;&#120;&#43;&#49;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"124\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-37725ebaefaa99a593c881c33fc7c8f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#110;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#110;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"136\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">56. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a25fbac68138db47e7e704e373511705_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#114;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#114;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"129\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f897468ddc6eadfb573fbd4e4f177a3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#121;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#121;&#45;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"145\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">58. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bb90fc3e75fdb3068f2a112705634957_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#109;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"142\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8a2b23ba902af2a61a64cc5cb6ccb53e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#113;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"128\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">60. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ae0309e565aea5eb855df6089dec8e5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#123;&#114;&#125;&#94;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#114;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"128\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9762d9fa6c730e676b2bb1b05938e6d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#122;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"160\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">62. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9e9d1a4a17837b91e44950ccd1c57a86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#48;&#120;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"163\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a3d3a3b17cb896de6553d4a41a289b17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#121;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"73\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">64. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a67cdb47d2200157407ebb83d3dd1f55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#98;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"71\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596387411\">Multiply a Binomial by a Binomial<\/h2>\n<p id=\"fs-id1168745394224\">In the following exercises, multiply the following binomials using: a) the Distributive Property b) the FOIL method c) the Vertical Method.<\/p>\n<div id=\"fs-id1169596387420\" data-type=\"exercise\">\n<div id=\"fs-id1169596387422\" data-type=\"problem\">\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-287832785f1f8fb2a7407fb983be0e3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#119;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#119;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%\">66. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-42b476926a1e38ece4c7471777a6fe06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">67. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-24830c49d23f4259ea7163afd6ca8de8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%\">68. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-27fd561904fbe163407ab051487b5fac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596387424\">In the following exercises, multiply the binomials. Use any method.<\/p>\n<\/div>\n<\/div>\n<table style=\"border-collapse: collapse;width: 100%;height: 140px\">\n<tbody>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">69. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-85b96522626577638475fe8957331401_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">70. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b8555b3e5d5aeb749b5aeee05200ca75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">71. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-286091540b754e39df972329a41e5ea0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">72. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-49b7315f0a29af03b4201124adbaa3a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">73. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-79575fe48044a878879482cbec42cbb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#119;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#119;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">74. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4ef673ba627b6babcea214d5b7d058ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">75. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f7f3283d24fe6f00a2c3568a32bde02e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">76. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-362ec555ca71f422f22bd2af13df101f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"130\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">77. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f63198d940195a2aebff7cf6358539c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#112;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">78. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-db169ddd7e7468a32e2d01f54b347ef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#109;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"130\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">79. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-61d32f7645cb05f4e76830eecd0c29c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#116;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#116;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">80. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d87f1671c30620929ce5a805a4726890_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#114;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#49;&#114;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">81. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5c5f8e9956db5fcc8c7069a2fd738d2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#120;&#45;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">82. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ab2fad34baf420786b0cba171f7329ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#97;&#45;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#97;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"134\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">83. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0ed55a29ad0f4defcbe1cc8dc8554642_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#97;&#43;&#51;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">84. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-98b3cf12f7b9fa0d0735ed2e95eb9e02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#43;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#114;&#43;&#50;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"123\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">85. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f0452e774129d489d7208a966a2f53fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#122;&#45;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">86. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3ea3bbe2db6248d3000b53eb4b732a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#120;&#45;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"119\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">87. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e5e3fb63494a007a196af8ea05fcd7e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"119\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">88. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-724b3c9011821e1841a43347fa4770ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"118\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">89. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-03b2083c348fd8acf0b7b98f95616d62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"128\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">90. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0b60ad3d401a1eceb5893a395b020f23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"127\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">91. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3024dcf839edca1b4b19a000c1480f49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#97;&#98;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#97;&#98;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%\">92. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7c8afa8f970ab333419bbb09403b1479_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#121;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#121;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">93. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9c7a6ca9095fafb3316e634fc6443349_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#112;&#113;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#112;&#113;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"143\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%\">94. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c50b7921d5cfb903f0fbca98d8435f33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#114;&#115;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#114;&#115;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"141\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596402196\"><strong data-effect=\"bold\"><br \/>\n<\/strong>Multiply a Trinomial by a Binomial<\/h2>\n<p id=\"fs-id1168742142113\">In the following exercises, multiply using a) the Distributive Property b) the Vertical Method.<\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">95. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4d291122545ac07d617751d721dcdaec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"160\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">96. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cdd0fede14c8d3a25d4f7776b53a048b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#117;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"160\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">97. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c42c7a9122c8fbb383000a84352874d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#121;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"157\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">98. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a56638ed16002ec02934c8b618163052_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#97;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"166\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1169596556594\" data-type=\"exercise\">\n<div id=\"fs-id1169596556596\" data-type=\"problem\">\n<p id=\"fs-id1169596556598\">In the following exercises, multiply. Use either method.<\/p>\n<\/div>\n<\/div>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">99. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-56367d9f4a47723822157fd44bffa6e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#119;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#45;&#57;&#119;&#43;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"178\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">100. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-afd03c9773145f98553772bf78d6599a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#112;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"156\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">101. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a512b348255527967e4030b9af13af35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#113;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#113;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"164\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">102. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3121b7a781dc47fdcbec2585cd6763e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#114;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#114;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"164\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1169596556256\" data-type=\"exercise\">\n<div id=\"fs-id1169596556258\" data-type=\"problem\">\n<h2 id=\"fs-id1169596556260\">Mixed Practice<\/h2>\n<\/div>\n<\/div>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">103. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6a3c66fca4406e2025aaf032be985e0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#121;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#121;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"154\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%\">104. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d794a778ce430b7eb98b7b18c9f7de7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#53;&#112;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#112;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"153\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">105. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e4d0f40a6b22e6865f045b01b7ee44b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#120;&#45;&#51;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#120;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"237\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">106. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8de2d1a00858b60c29fdae368ab77139_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#106;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#106;&#45;&#50;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#106;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#106;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"239\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">107. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0236331b63ca60e2b8e1b241eaae215c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#113;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#113;&#43;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"138\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">108. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-29dbd3bfd119bd89ed7060c8849f42a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#116;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#116;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"123\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">109. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ea98546d147c3f738947d8290463ffd8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#115;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#115;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%\">110. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3d78c5db225363ff6406f0bfe248679a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#49;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"119\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">111. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1e376d8c37db08359948f178e08b5f2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"127\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">112. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-41b23f064200865c4543b2bdcca61009_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#97;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"136\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">113. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ff7637e2481c43c32316055047b0ff24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#110;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#43;&#110;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"161\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">114. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6edfe8d0ff78937196ec2254ded6ba4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#107;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#107;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#107;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"168\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">115. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9f00ab8881ae5808106c0bce8333ad9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#112;&#43;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#112;&#45;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"143\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%\">116. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1d54a261f366bd301d5f79c8dda89d2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#121;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#121;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">117. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1bda7e19ac65beca4b33bf94ec1f6b6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#109;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#109;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"149\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">118. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-032fdfc7e2b29739ceb16e791e2a451a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#53;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#99;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#99;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"134\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">119. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e2ec1757ddcf41a77e83c02bbe35e13b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#97;&#43;&#55;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#97;&#43;&#55;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%\">120. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-17a124aa246b76df575b79808dbdad85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#45;&#49;&#49;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#45;&#49;&#49;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"164\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">121. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3d037e403e858ee2c9256b17d90f0989_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#121;&#43;&#49;&#50;&#122;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#121;&#45;&#49;&#50;&#122;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"162\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 style=\"text-align: left\" data-type=\"title\">Everyday Math<\/h2>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">\n<p id=\"fs-id1169596398985\">122.<strong> Mental math<\/strong> You can use binomial multiplication to multiply numbers without a calculator. Say you need to multiply 13 times 15. Think of 13 as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4cc6f21669f8c411c8ef3b3d9428ef3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"47\" style=\"vertical-align: -2px;\" \/> and 15 as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dca5084fa1508710302a9184b979a6e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"46\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<ol id=\"fs-id1168742188094\" class=\"circled\" type=\"a\">\n<li>Multiply <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9d6ff14c27209d5b35873ea590d8ab9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"125\" style=\"vertical-align: -5px;\" \/> by the FOIL method.<\/li>\n<li>Multiply <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e1c2ab71241a1348a3b19401c34b28a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"47\" style=\"vertical-align: 0px;\" \/> without using a calculator.<\/li>\n<li>Which way is easier for you? Why?<\/li>\n<\/ol>\n<\/td>\n<td style=\"width: 50%\">\n<p id=\"fs-id1169596498098\">123.<strong data-effect=\"bold\"> Mental math<\/strong> You can use binomial multiplication to multiply numbers without a calculator. Say you need to multiply 18 times 17. Think of 18 as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b94ace3cbf71f31ee28cf5833077c3b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/> and 17 as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-364ab5ab5bf5dc005c739a076c6e4624_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<ol id=\"fs-id1168742196535\" class=\"circled\" type=\"a\">\n<li>Multiply <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-46923645fb06f0a7a0a21e7661169f57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#48;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#48;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"125\" style=\"vertical-align: -5px;\" \/> by the FOIL method.<\/li>\n<li>Multiply <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b578058b3fb1c57bcca246cf9c454d21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"48\" style=\"vertical-align: 0px;\" \/> without using a calculator.<\/li>\n<li>Which way is easier for you? Why?<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 style=\"text-align: left\" data-type=\"title\">Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">124. Which method do you prefer to use when multiplying two binomials: the Distributive Property, the FOIL method, or the Vertical Method? Why?<\/td>\n<td style=\"width: 50%\">125. Which method do you prefer to use when multiplying a trinomial by a binomial: the Distributive Property or the Vertical Method? Why?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">\n<p id=\"fs-id1169596554478\">126. Multiply the following:<\/p>\n<p id=\"fs-id1169596554482\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-30c33b4cac2d7df29a9caee63d472408_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#119;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#119;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"116\" style=\"vertical-align: -27px;\" \/><\/p>\n<p id=\"fs-id1169596411012\">Explain the pattern that you see in your answers.<\/p>\n<\/td>\n<td style=\"width: 50%\">\n<p id=\"fs-id1169596411028\">127. Multiply the following:<\/p>\n<p id=\"fs-id1169596411031\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1045a38ef56ce8aa7d5c48dfb66a2db7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#43;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"129\" style=\"vertical-align: -27px;\" \/><\/p>\n<p id=\"fs-id1169596387870\">Explain the pattern that you see in your answers.<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">\n<p id=\"fs-id1169596387886\">128. Multiply the following:<\/p>\n<p id=\"fs-id1169596387889\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c3871932d9db5d62920e4d08eef6cded_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"108\" style=\"vertical-align: -27px;\" \/><\/p>\n<p id=\"fs-id1169596387994\">Explain the pattern that you see in your answers.<\/p>\n<\/td>\n<td style=\"width: 50%\">\n<p id=\"fs-id1169596556729\">129. Multiply the following:<\/p>\n<p id=\"fs-id1169596556732\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d05c51c7e4de232ca0e759837ddd2d0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"110\" style=\"vertical-align: -27px;\" \/><\/p>\n<p id=\"fs-id1169596556837\">Explain the pattern that you see in your answers.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1 style=\"text-align: left\">Answers<\/h1>\n<table style=\"border-collapse: collapse;width: 100%;height: 320px\">\n<tbody>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">1. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0a4d1644531cb05807e1f28748db532b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#119;&#43;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"62\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ef223637152312f18e6ce8e4f3a1762e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#97;&#45;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"70\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a2628e7d3f8f01057195073a4c7e4330_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"59\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-81ca5fdfa08c316d8b67e91d35d43c3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#107;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"70\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b19e11539202122a50b7896769681f40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b4c68e448ca31c0172988630f6cea029_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#57;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-89c5a8d9995415f4d7cd6de3f8799b6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#125;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#48;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"73\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9f6ca1ed8152e5fc9c64f5aa2735270c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#114;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"81\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-295064e1c5c31465f81886ffcd5e57b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#50;&#48;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"93\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7f36fd430002e660762ff2b253ef94a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#55;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#53;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"96\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2dbaae5459c0b4df12a2019e1e986e0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#48;&#112;&#43;&#55;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c0876d02fbfd047746f3ebbe9ffcd252_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#48;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"155\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f72ead2fc2c89b02bbcf2dbedf408468_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#113;&#125;&#94;&#123;&#54;&#125;&#45;&#49;&#48;&#123;&#113;&#125;&#94;&#123;&#52;&#125;&#43;&#51;&#48;&#123;&#113;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9edb916b3a87ea80fd734ff16d71ff12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#48;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"153\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0950ea6808ad1bed24bd4700e448cd71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#113;&#125;&#94;&#123;&#53;&#125;&#45;&#49;&#48;&#123;&#113;&#125;&#94;&#123;&#52;&#125;&#43;&#51;&#48;&#123;&#113;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3ad012d27ea9dfd469cd2b8777e768f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#123;&#122;&#125;&#94;&#123;&#52;&#125;&#45;&#52;&#56;&#123;&#122;&#125;&#94;&#123;&#51;&#125;&#43;&#52;&#123;&#122;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"150\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-79e3ddb76974472e6d2f0c33bdf08a48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#57;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"78\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-82614f0fb37d97ddff6f6303a6816eef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#119;&#45;&#52;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"62\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0b4ba70fb63870f9089ba3045f1176d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"59\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cd435374bba42b49c8b1d3f9d8ff5f35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#114;&#45;&#51;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"74\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0acf2a364d8fe1e3d6f63e35ab077935_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#109;&#45;&#51;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"77\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6f1b0392002c918e95357e195a00b814_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#122;&#43;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"70\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c16cb2050227864306bc5416016af4a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#117;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"59\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-487e7b8fc9e7b6ab103429b6d26eaf33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#45;&#51;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"67\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2165ea2be054a82fb20a6af9df73e747_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#120;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f88a60bfef0fdca466ac666a1f4517ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#53;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#53;&#112;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6580076dc85dc065455e8f85b36dfd52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#48;&#118;&#43;&#55;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"113\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-31de27044338b5c3f98c64ee2effb827_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#45;&#56;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"118\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9edb916b3a87ea80fd734ff16d71ff12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#48;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"153\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0950ea6808ad1bed24bd4700e448cd71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#113;&#125;&#94;&#123;&#53;&#125;&#45;&#49;&#48;&#123;&#113;&#125;&#94;&#123;&#52;&#125;&#43;&#51;&#48;&#123;&#113;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3ad012d27ea9dfd469cd2b8777e768f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#123;&#122;&#125;&#94;&#123;&#52;&#125;&#45;&#52;&#56;&#123;&#122;&#125;&#94;&#123;&#51;&#125;&#43;&#52;&#123;&#122;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"150\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2cf0f505154abfa2900b0019100b53ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#57;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5c25bcf5752ee3ec1e7779f56b381737_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#119;&#43;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"112\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">67. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-88aaab23e11e09f2a2e66c262f0e3cb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#112;&#45;&#52;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">69. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cc07d1cef2d6aa9b36619f8bcf2eea5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#49;&#120;&#43;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"107\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">71. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dd82c9c53a0245256bf1caeb2405dcd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#121;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">73. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e0a8b93ceab484a4357cb200872075da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#119;&#45;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"104\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">75. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-477eeea1fbef0afee4b4606ac9e20025_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#112;&#45;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">77. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-64802ba8b1064e22f1df9a46d2b81aef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#49;&#112;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">79. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1c60dec55b0b8752d2ef6a06666ea28f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#56;&#116;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"108\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">81. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-af29cce96f04882c9e98339777d7d5b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#121;&#45;&#51;&#48;&#120;&#43;&#54;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"174\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%\">83. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9137afe6d69c7e1a07b1ef4d30c21a6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#97;&#98;&#43;&#51;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"119\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">85. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b0a0b33449652abf93a5e40698f5e635_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#52;&#122;&#45;&#122;&#121;&#43;&#54;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"154\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%\">87. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e5748effc563a458b765e64fff549d70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#43;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"138\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">89. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bb639d723cb06664f56843281840bf73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#43;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"106\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%\">91. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-aa716f352b46dac9e73d79237377679e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#51;&#97;&#98;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"136\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">93. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8e23681052d75c788ee11f658b235373_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#50;&#112;&#113;&#43;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%\">95. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4df784ec16c91c7e5bf276f71a91738c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#43;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#51;&#120;&#43;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"154\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">97. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f0ae393aadf6cadb46c64d3f247431f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#43;&#51;&#51;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#121;&#45;&#53;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"153\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%\">99. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0d3bca0e5da266029556e46d2cb0eaa1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#119;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#54;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#51;&#119;&#45;&#55;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"173\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">101. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-46c24a3228cf450ef3161b12aea70762_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#49;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#57;&#113;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"158\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%\">103. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2aace44b3bf7a2df6666dd64c8c83db9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#121;&#45;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">105. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4a7ad0c8f06846a288709feeb15068d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;&#120;&#45;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"80\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%\">107. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ff908f4bdf369689dac11dad4b1f836d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#45;&#51;&#48;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#53;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">109. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4c324233f6263cca1e10aae1a55b1e0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#115;&#45;&#54;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"95\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%\">111. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-082d0d78a96590df403910a7a55cfc62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#45;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">113. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d2b88be81f4ff7fae27b672e197b6213_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#45;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#53;&#110;&#43;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"157\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%\">115. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cfcadb12330220c1b4a13811e760127c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#57;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">117. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-92c60f46b9605658bc609d24998c1d55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#109;&#125;&#94;&#123;&#52;&#125;&#45;&#51;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#45;&#55;&#123;&#109;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"140\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%\">119. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ed55bbc5198946953c250faea1b76b2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#48;&#97;&#98;&#43;&#52;&#57;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"146\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">121. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-903c3ada8bea27bf7578ee6472f6ddd8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#52;&#52;&#123;&#122;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"98\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%\">123. a) 306 b) 306 c) Answers will vary.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">125. Answers will vary.<\/td>\n<td style=\"width: 50%\">127.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dd808300d9bc0a500f1c4d08a49a2153_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#50;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-941e65cc9e3659acc63c3b85c7a7ceb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#110;&#125;&#94;&#50;&#45;&#49;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"67\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-08685cffda4480f9e93581f1b32b2658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#50;&#45;&#54;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"57\" style=\"vertical-align: -4px;\" \/><br \/>\nAnswers will vary.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">129.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2a6a787ee090419f1f3149114277305c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#50;&#45;&#56;&#120;&#43;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -2px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-13d913fcaa77fb73925ecbacdfc6c7b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#50;&#45;&#50;&#121;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"87\" style=\"vertical-align: -4px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f52b606ae724ecf265a1862af75a446e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#122;&#125;&#94;&#50;&#45;&#49;&#52;&#122;&#43;&#52;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"105\" style=\"vertical-align: -2px;\" \/><br \/>\nAnswers will vary.<\/td>\n<td style=\"width: 50%\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cMultiply Polynomials\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n<p><!-- pb_fixme --><\/p>\n","protected":false},"author":999,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[48],"contributor":[],"license":[],"class_list":["post-1772","chapter","type-chapter","status-publish","hentry","chapter-type-numberless"],"part":1647,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1772","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/users\/999"}],"version-history":[{"count":25,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1772\/revisions"}],"predecessor-version":[{"id":2655,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1772\/revisions\/2655"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/parts\/1647"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1772\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/media?parent=1772"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapter-type?post=1772"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/contributor?post=1772"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/license?post=1772"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}