{"id":2196,"date":"2022-08-05T18:15:14","date_gmt":"2022-08-05T18:15:14","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math53\/?post_type=chapter&#038;p=2196"},"modified":"2023-07-13T01:36:04","modified_gmt":"2023-07-13T01:36:04","slug":"6-7-factor-binomials-difference-of-squares","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math53\/chapter\/6-7-factor-binomials-difference-of-squares\/","title":{"raw":"6.7 Factor Binomials - Difference of Squares","rendered":"6.7 Factor Binomials &#8211; Difference of Squares"},"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>Factor Binomials of the Form a<sup>2<\/sup>x<sup>2<\/sup> \u2013 b<sup>2<\/sup>y<sup>2<\/sup><\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169596391251\">Let us first review briefly what we learned in <a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/chapter\/special-products\/\" target=\"_blank\" rel=\"noopener\">Chapter 6.3<\/a>:<\/p>\r\n\r\n<div id=\"fs-id1169596391023\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Product of Conjugates Pattern<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1169596391028\">If \\(a\\) and \\(b\\) are real numbers,<\/p>\r\n<span id=\"fs-id1169596367551\" data-type=\"media\" data-alt=\"This figure is divided into two sides. On the left side is the following formula: the product of a minus b and a plus b equals a squared minus b squared. On the right side is the same formula labeled: a minus b and a plus b are labeled \u201cconjugates\u201d, the a squared and b squared are labeled squares and the minus sign between the squares is labeled \u201cdifference\u201d. Therefore, the product of two conjugates is called a difference of squares.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/comp030\/wp-content\/uploads\/sites\/1048\/2021\/05\/CNX_ElemAlg_Figure_06_04_020_img_new.jpg\" alt=\"This figure is divided into two sides. On the left side is the following formula: the product of a minus b and a plus b equals a squared minus b squared. On the right side is the same formula labeled: a minus b and a plus b are labeled \u201cconjugates\u201d, the a squared and b squared are labeled squares and the minus sign between the squares is labeled \u201cdifference\u201d. Therefore, the product of two conjugates is called a difference of squares.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<\/div>\r\nThe product is called a difference of squares.\r\n\r\n<\/div>\r\n<h1>Factor the Difference of Squares<\/h1>\r\n<p id=\"fs-id1169596566014\">To be more specific, we are going to see how we can factorize the difference of <strong>two<\/strong> squares. From above, it is very clear that factors of a binomial of the type\u00a0 \\({a}^{2}-{b}^{2}\\) are always \\(\\left(a+b\\right)\\left(a-b\\right)\\). Once we know what \\(a\\) and \\(b\\)\u00a0are, the factorization becomes very easy.<\/p>\r\n\r\n<\/div>\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-id1169596404708\" data-type=\"problem\">\r\n<p id=\"fs-id1169596404710\">Factor the difference of square: \\({x}^{2}-{64}\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596403359\" 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-id1169596403364\">First, we rewrite each term of \\({x}^{2}-{64}\\) as a perfect square of an expression.<\/p>\r\n\r\n<table id=\"eip-id1172188052941\" 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 text in the left column says \u201cIt fits the pattern.\u201d The right column contains the product of x minus 8, in parentheses, and x plus 8, in parentheses. Above this is the general form a minus b, in parentheses, times a plus b, in parentheses. In the second row, the left column says \u201cSquare the first term, x.\u201d The right column contains x squared minus blank. Above this is the general form a squared minus b squared. In the third row, the text on the left says \u201cSquare the last term, 8.\u201d The right column contains the expression x squared minus 8 squared. Above this is the general form a squared minus b squared. In the last row, the text in the left column says \u201cThe product is a difference of squares.\u201d The right column contains the expression x squared minus 64. Above this is the general form a squared minus b squared.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 314.994px\">Rewrite each term as a perfect square<\/td>\r\n<td style=\"width: 266.987px\"><img class=\"alignnone size-medium wp-image-2539\" src=\"https:\/\/pressbooks.bccampus.ca\/comp030\/wp-content\/uploads\/sites\/1048\/2022\/08\/Example-1-_pic1-1-300x75.png\" alt=\"\" width=\"300\" height=\"75\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 314.994px\">Treating [latex]x[\/latex] as [latex]a[\/latex] and [latex]8[\/latex] as [latex]b[\/latex]<\/td>\r\n<td style=\"width: 266.987px\"><img class=\"alignnone size-medium wp-image-2542\" src=\"https:\/\/pressbooks.bccampus.ca\/comp030\/wp-content\/uploads\/sites\/1048\/2022\/08\/Example-1-_pic2-1-300x75.png\" alt=\"\" width=\"300\" height=\"75\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 314.994px\">Apply the difference of squares formula<\/td>\r\n<td style=\"width: 266.987px\"><span id=\"eip-id1172188052961\" data-type=\"media\" data-alt=\"The product of x minus 8 and x plus 8. Above this is the general form a minus b, in parentheses, times a plus b, in parentheses.\"><img class=\"alignnone size-medium wp-image-2544\" src=\"https:\/\/pressbooks.bccampus.ca\/comp030\/wp-content\/uploads\/sites\/1048\/2022\/08\/Example-1-_pic3-300x75.png\" alt=\"\" width=\"300\" height=\"75\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 314.994px\">Hence,<\/td>\r\n<td style=\"width: 266.987px\">\\({x}^{2}-{64}\\) [latex]=(x+8)(x-8)[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Difference of Squares<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1169596391028\">If \\(a\\) and \\(b\\) are real numbers, then<\/p>\r\n<img class=\"wp-image-2564 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/comp030\/wp-content\/uploads\/sites\/1048\/2022\/08\/diff_of_squares-300x75.png\" alt=\"difference of squares formula\" width=\"264\" height=\"66\" \/>\r\n\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-id1169596382320\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596376846\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596376848\" data-type=\"problem\">\r\n\r\nFactor:\u00a0[latex]n^2 - 49[\/latex]\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596308784\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596569338\">[latex](n+7)(n-7)[\/latex]<\/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 1.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596568300\" data-type=\"problem\">\r\n<p id=\"fs-id1169596568302\">Factor: \\({w}^{2}-9\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596569446\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596569448\">\\(\\left(w+3\\right)\\left(w-3\\right)\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596568294\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596568297\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596569446\" 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-id1169596361165\" data-type=\"problem\">\r\n\r\nFactor completely: \\(4{m}^{2}-81\\).\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596392529\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596403359\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1169596403364\">We know that [latex]4m^2 = (2m)^2[\/latex] and [latex]81 = 9^2[\/latex]<\/p>\r\n\r\n<table id=\"eip-id1172188052941\" 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 text in the left column says \u201cIt fits the pattern.\u201d The right column contains the product of x minus 8, in parentheses, and x plus 8, in parentheses. Above this is the general form a minus b, in parentheses, times a plus b, in parentheses. In the second row, the left column says \u201cSquare the first term, x.\u201d The right column contains x squared minus blank. Above this is the general form a squared minus b squared. In the third row, the text on the left says \u201cSquare the last term, 8.\u201d The right column contains the expression x squared minus 8 squared. Above this is the general form a squared minus b squared. In the last row, the text in the left column says \u201cThe product is a difference of squares.\u201d The right column contains the expression x squared minus 64. Above this is the general form a squared minus b squared.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 314.994px\">Rewrite each term as a perfect square<\/td>\r\n<td style=\"width: 266.987px\">[latex](2m)^2 - 9^2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 314.994px\">Treating [latex]2m[\/latex] as [latex]a[\/latex] and [latex]9[\/latex] as [latex]b[\/latex]<\/td>\r\n<td style=\"width: 266.987px\">[latex]a = 2m , b = 9[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 314.994px\">Apply the difference of squares formula [latex]a^2 -b^2 = (a+b)(a-b)[\/latex]<\/td>\r\n<td style=\"width: 266.987px\">[latex](2m+9)(2m-9)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 314.994px\">Hence,<\/td>\r\n<td style=\"width: 266.987px\">\\(4{m}^{2}-81\\) [latex]=(2m+9)(2m-9)[\/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-id1169596566475\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596566479\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596555445\" data-type=\"problem\">\r\n<p id=\"fs-id1169596555447\">Factor completely: \\(36{x}^{2}-49\\) .<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596308819\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596308821\">\\(\\left(6x+7\\right)\\left(6x-7\\right)\\)<\/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 2.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596366001\" data-type=\"problem\">\r\n<p id=\"fs-id1169596381369\">Factor completely: \\(49{x}^{2}-\\dfrac{25}{121}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596404475\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596404477\">\\(\\left(7x+\\dfrac{5}{11}\\right)\\left(7x-\\dfrac{5}{11}\\right)\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\nNow we\u2019ll factor a similar binomial that has two variables.\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-id1169596276239\" data-type=\"problem\">\r\n<div id=\"fs-id1169596361165\" data-type=\"problem\">\r\n\r\nFactor completely: \\(25{x}^{2}-{y}^2\\).\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596392529\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596403359\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1169596403364\">We know that [latex]25=5^2[\/latex], [latex]x^2 = (x)^2[\/latex] and [latex]y^2 = (y)^2[\/latex]<\/p>\r\n\r\n<table id=\"eip-id1172188052941\" 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 text in the left column says \u201cIt fits the pattern.\u201d The right column contains the product of x minus 8, in parentheses, and x plus 8, in parentheses. Above this is the general form a minus b, in parentheses, times a plus b, in parentheses. In the second row, the left column says \u201cSquare the first term, x.\u201d The right column contains x squared minus blank. Above this is the general form a squared minus b squared. In the third row, the text on the left says \u201cSquare the last term, 8.\u201d The right column contains the expression x squared minus 8 squared. Above this is the general form a squared minus b squared. In the last row, the text in the left column says \u201cThe product is a difference of squares.\u201d The right column contains the expression x squared minus 64. Above this is the general form a squared minus b squared.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 314.994px\">Rewrite each term as a perfect square<\/td>\r\n<td style=\"width: 266.987px\">[latex](5x)^2 - (y)^2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 314.994px\">Assigning values to \\(a\\) and \\(b\\)<\/td>\r\n<td style=\"width: 266.987px\">[latex]a = 5x , b = y[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 314.994px\">Apply the difference of squares formula [latex]a^2 -b^2 = (a+b)(a-b)[\/latex]<\/td>\r\n<td style=\"width: 266.987px\">[latex](5x+y)(5x-y)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 314.994px\">Hence,<\/td>\r\n<td style=\"width: 266.987px\">[latex]25x^2 - y^2 = (5x+y)(5x-y)[\/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 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-id1169596574039\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596574042\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596574044\" data-type=\"problem\">\r\n<p id=\"fs-id1169596574046\">Factor: \\(49{y}^2-16{x}^{2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596391449\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596391451\">\\(\\left(7y+4x\\right)\\left(7y-4x\\right)\\)<\/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 3.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596393084\" data-type=\"problem\">\r\n<p id=\"fs-id1169596393086\">Factor: \\(81{m}^2-4{n}^{2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596455633\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596455635\">\\(\\left(9m+2n\\right)\\left(9m-2n\\right)\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596392876\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596392880\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596555078\" 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-id1169596360904\" data-type=\"problem\">\r\n<div id=\"fs-id1169596361165\" data-type=\"problem\">\r\n\r\nFactor completely: \\(25{x}^{2}{y}^2 - 36\\).\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596392529\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596403359\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1169596403364\">We know that [latex]25=5^2[\/latex], [latex]x^2 = (x)^2[\/latex] , [latex]y^2 = (y)^2[\/latex] and [latex]36 = 6^2[\/latex]<\/p>\r\n\r\n<table id=\"eip-id1172188052941\" 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 text in the left column says \u201cIt fits the pattern.\u201d The right column contains the product of x minus 8, in parentheses, and x plus 8, in parentheses. Above this is the general form a minus b, in parentheses, times a plus b, in parentheses. In the second row, the left column says \u201cSquare the first term, x.\u201d The right column contains x squared minus blank. Above this is the general form a squared minus b squared. In the third row, the text on the left says \u201cSquare the last term, 8.\u201d The right column contains the expression x squared minus 8 squared. Above this is the general form a squared minus b squared. In the last row, the text in the left column says \u201cThe product is a difference of squares.\u201d The right column contains the expression x squared minus 64. Above this is the general form a squared minus b squared.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 314.994px\">Rewrite each term as a perfect square<\/td>\r\n<td style=\"width: 266.987px\">[latex](5xy)^2 - (6)^2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 314.994px\">Assigning values to \\(a\\) and \\(b\\)<\/td>\r\n<td style=\"width: 266.987px\">[latex]a = 5xy , b = 6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 314.994px\">Apply the difference of squares formula [latex]a^2 -b^2 = (a+b)(a-b)[\/latex]<\/td>\r\n<td style=\"width: 266.987px\">[latex](5xy+6)(5xy-6)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 314.994px\">Hence,<\/td>\r\n<td style=\"width: 266.987px\">[latex]25x^2y^2 - 36 = (5xy+6)(5xy-6)[\/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 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-id1169596303932\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596303936\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596303938\" data-type=\"problem\">\r\n<p id=\"fs-id1169596303940\">Factor: \\({x}^{2}{y}^{2}-1\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596566590\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596566592\">\\(\\left(xy-1\\right)\\left(xy+1\\right)\\)<\/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 4.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596574406\" data-type=\"problem\">\r\n<p id=\"fs-id1169596574408\">Factor: \\({a}^{2}{b}^{2}-81\\) .<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596366993\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596366995\">\\(\\left(ab-9\\right)\\left(ab+9\\right)\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\nLet us now try to factor a binomial where it is not apparent that we can use the Difference of Squares formula right away.\r\n<div id=\"fs-id1169596574400\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596574404\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596366993\" 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-id1169596569315\" data-type=\"problem\">\r\n<p id=\"fs-id1169596569317\">Factor: [latex]3a^2 - 27b^2[\/latex]<\/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<p id=\"fs-id1169596403364\">We know that\u00a0 [latex]a^2 = (a)^2[\/latex] and [latex]b^2 = (b)^2[\/latex] but neither 3 nor 27 is a perfect square. In a question like this check whether the numbers have a GCF other than 1. In this case, the GCF of 3 and 27 is 3.\u00a0 Now apply your knowledge of factoring out the GCF and check if you can factor the binomial any further:<\/p>\r\n\r\n<table id=\"eip-id1172188052941\" 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 text in the left column says \u201cIt fits the pattern.\u201d The right column contains the product of x minus 8, in parentheses, and x plus 8, in parentheses. Above this is the general form a minus b, in parentheses, times a plus b, in parentheses. In the second row, the left column says \u201cSquare the first term, x.\u201d The right column contains x squared minus blank. Above this is the general form a squared minus b squared. In the third row, the text on the left says \u201cSquare the last term, 8.\u201d The right column contains the expression x squared minus 8 squared. Above this is the general form a squared minus b squared. In the last row, the text in the left column says \u201cThe product is a difference of squares.\u201d The right column contains the expression x squared minus 64. Above this is the general form a squared minus b squared.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 314.994px\">Factor out the GCF<\/td>\r\n<td style=\"width: 266.987px\">[latex]3(a^2 -9b^2)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 314.994px\">Rewrite each term as a perfect square<\/td>\r\n<td style=\"width: 266.987px\">[latex]3((a)^2 - (3b)^2)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 314.994px\">Assigning values to \\(a\\) and \\(b\\)<\/td>\r\n<td style=\"width: 266.987px\">[latex]a = a , b = 3b[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 314.994px\">Apply the difference of squares formula [latex]a^2 -b^2 = (a+b)(a-b)[\/latex]<\/td>\r\n<td style=\"width: 266.987px\">[latex]3(a+3b)(a-3b)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 314.994px\">Hence,<\/td>\r\n<td style=\"width: 266.987px\">[latex]3a^2 - 27b^2 = 3(a+3b)(a-3b)[\/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-id1169596302415\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596302419\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\r\n<p id=\"fs-id1169596302423\">Factor completely: [latex]36x^2-9y^2[\/latex]<\/p>\r\n\r\n<\/div>\r\n<details open=\"open\"><summary>Show answer<\/summary>\r\n<div id=\"fs-id1169596303989\" data-type=\"solution\">[latex]9(2x+y)(2x-y)[\/latex]<\/div>\r\n<\/details>&nbsp;\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 5.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596304022\" data-type=\"problem\">\r\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\r\n<p id=\"fs-id1169596302423\">Factor completely: [latex]3.6x^2-0.9[\/latex]<\/p>\r\n\r\n<\/div>\r\n<details open=\"open\"><summary>Show answer<\/summary>\r\n<div id=\"fs-id1169596303989\" data-type=\"solution\">[latex]0.9(2x+1)(2x-1)[\/latex]<\/div>\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596574400\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596574404\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596366993\" 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-id1169596569315\" data-type=\"problem\">\r\n<p id=\"fs-id1169596569317\">Factor: [latex]x^4 - y^6[\/latex]<\/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<p id=\"fs-id1169596403364\">We know that\u00a0 [latex]x^4 = (x^2)^2[\/latex] and [latex]y^6 = (y^3)^2[\/latex]<\/p>\r\n\r\n<table id=\"eip-id1172188052941\" class=\"unnumbered unstyled\" style=\"height: 91px\" summary=\"This figure 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 fits the pattern.\u201d The right column contains the product of x minus 8, in parentheses, and x plus 8, in parentheses. Above this is the general form a minus b, in parentheses, times a plus b, in parentheses. In the second row, the left column says \u201cSquare the first term, x.\u201d The right column contains x squared minus blank. Above this is the general form a squared minus b squared. In the third row, the text on the left says \u201cSquare the last term, 8.\u201d The right column contains the expression x squared minus 8 squared. Above this is the general form a squared minus b squared. In the last row, the text in the left column says \u201cThe product is a difference of squares.\u201d The right column contains the expression x squared minus 64. Above this is the general form a squared minus b squared.\" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 314.98px;height: 15px\">Factor out the GCF (if any)<\/td>\r\n<td style=\"width: 266.987px;height: 15px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 314.98px;height: 15px\">Rewrite each term as a perfect square<\/td>\r\n<td style=\"width: 266.987px;height: 15px\">[latex]((x^2)^2 - (y^3)^2)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 314.98px;height: 15px\">Assigning values to \\(a\\) and \\(b\\)<\/td>\r\n<td style=\"width: 266.987px;height: 15px\">[latex]a = x^2 , b = y^3[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 31px\">\r\n<td style=\"width: 314.98px;height: 31px\">Apply the difference of squares formula [latex]a^2 -b^2 = (a+b)(a-b)[\/latex]<\/td>\r\n<td style=\"width: 266.987px;height: 31px\">[latex](x^2+y^3)(x^2-y^3)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 314.98px;height: 15px\">Hence,<\/td>\r\n<td style=\"width: 266.987px;height: 15px\">[latex]x^4 - y^6 =\u00a0 (x^2+y^3)(x^2-y^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 6.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596302415\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596302419\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\r\n<p id=\"fs-id1169596302423\">Factor completely: [latex]x^4 - 9[\/latex]<\/p>\r\n\r\n<\/div>\r\n<details open=\"open\"><summary>Show answer<\/summary>\r\n<div id=\"fs-id1169596303989\" data-type=\"solution\">[latex](x^2+3)(x^2-3)[\/latex]<\/div>\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 6.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596302415\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596302419\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\r\n<p id=\"fs-id1169596302423\">Factor completely: [latex]2m^4n^2 - 50[\/latex]<\/p>\r\n\r\n<\/div>\r\n<details open=\"open\"><summary>Show answer<\/summary>\r\n<div id=\"fs-id1169596303989\" data-type=\"solution\">[latex]2(m^2n+5)(m^2n-5)[\/latex]<\/div>\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Can you factor Sum of Squares?<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">Note that, except for a common factor, a sum of squares or a binomial of the form [latex]a^2 + b^2[\/latex] is not factorable over the set of real numbers.<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596574400\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596574404\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596366993\" data-type=\"solution\">\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-id1169596569315\" data-type=\"problem\">\r\n<p id=\"fs-id1169596569317\">Factor completely: [latex]x^4 - 16[\/latex]<\/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<p id=\"fs-id1169596403364\">We know that\u00a0 [latex]x^4 = (x^2)^2[\/latex] and [latex]16 = (4)^2[\/latex]<\/p>\r\n\r\n<table id=\"eip-id1172188052941\" class=\"unnumbered unstyled\" style=\"height: 91px\" summary=\"This figure 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 fits the pattern.\u201d The right column contains the product of x minus 8, in parentheses, and x plus 8, in parentheses. Above this is the general form a minus b, in parentheses, times a plus b, in parentheses. In the second row, the left column says \u201cSquare the first term, x.\u201d The right column contains x squared minus blank. Above this is the general form a squared minus b squared. In the third row, the text on the left says \u201cSquare the last term, 8.\u201d The right column contains the expression x squared minus 8 squared. Above this is the general form a squared minus b squared. In the last row, the text in the left column says \u201cThe product is a difference of squares.\u201d The right column contains the expression x squared minus 64. Above this is the general form a squared minus b squared.\" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 314.98px;height: 15px\">Factor out the GCF (if any)<\/td>\r\n<td style=\"width: 266.987px;height: 15px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 314.98px;height: 15px\">Rewrite each term as a perfect square<\/td>\r\n<td style=\"width: 266.987px;height: 15px\">[latex]((x^2)^2 - (4)^2)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 314.98px;height: 15px\">Assigning values to \\(a\\) and \\(b\\)<\/td>\r\n<td style=\"width: 266.987px;height: 15px\">[latex]a = x^2 , b =4[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 31px\">\r\n<td style=\"width: 314.98px;height: 31px\">Apply the difference of squares formula [latex]a^2 -b^2 = (a+b)(a-b)[\/latex]<\/td>\r\n<td style=\"width: 266.987px;height: 31px\">[latex](x^2+4)(x^2-4)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 31px\">\r\n<td colspan=\"2\"><strong>So far, this question is not much different from the previous examples but note that this factorization is incomplete. Why? Because the second factor [latex](x^2-4)[\/latex] can also be rewritten as a difference of squares. The first factor [latex](x^2+4)[\/latex] is a sum of squares and cannot be factored further over the set of real numbers.\u00a0<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 314.98px;height: 15px\">Rewrite each term of the second factor as a perfect square<\/td>\r\n<td style=\"width: 266.987px;height: 15px\">[latex](x^2+4)((x)^2 - (2)^2)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 314.98px;height: 15px\">Assigning values to \\(a\\) and \\(b\\)<\/td>\r\n<td style=\"width: 266.987px;height: 15px\">[latex]a = x , b =2[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 31px\">\r\n<td style=\"width: 314.98px;height: 31px\">Apply the difference of squares formula [latex]a^2 -b^2 = (a+b)(a-b)[\/latex]<\/td>\r\n<td style=\"width: 266.987px;height: 31px\">[latex](x^2+4)(x+2)(x-2)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 314.98px;height: 15px\">Hence,<\/td>\r\n<td style=\"width: 266.987px;height: 15px\">[latex]x^4 - 16 =\u00a0 (x^2+4)(x+2)(x-2)[\/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<div id=\"fs-id1169596304022\" data-type=\"problem\">\r\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\r\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\r\n<p id=\"fs-id1169596302423\">Factor completely: [latex]y^4 - 81[\/latex]<\/p>\r\n\r\n<\/div>\r\n<details open=\"open\"><summary>Show answer<\/summary>\r\n<div id=\"fs-id1169596303989\" data-type=\"solution\">[latex](y^2 +9)(y+3)(y-3)[\/latex]<\/div>\r\n<\/details><\/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 7.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596304022\" data-type=\"problem\">\r\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\r\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\r\n<p id=\"fs-id1169596302423\">Factor completely: [latex]5p^4 - 80[\/latex]<\/p>\r\n\r\n<\/div>\r\n<details open=\"open\"><summary>Show answer<\/summary>\r\n<div id=\"fs-id1169596303989\" data-type=\"solution\">[latex]5(p^2 + 4)(p+2)(p-2)[\/latex]<\/div>\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596574400\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596574400\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596574404\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596366993\" 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-id1169596569315\" data-type=\"problem\">\r\n<p id=\"fs-id1169596569317\">Factor completely: [latex]36-(x-5)^2[\/latex]<\/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<p id=\"fs-id1169596403364\">We can apply the difference of squares formula not only on monomials that are perfect squares but also on any polynomial that is a perfect square. In this example, we know that\u00a0 [latex]36 = (6)^2[\/latex] and the second term is already in the form of a perfect square.<\/p>\r\n\r\n<table id=\"eip-id1172188052941\" class=\"unnumbered unstyled\" style=\"height: 91px\" summary=\"This figure 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 fits the pattern.\u201d The right column contains the product of x minus 8, in parentheses, and x plus 8, in parentheses. Above this is the general form a minus b, in parentheses, times a plus b, in parentheses. In the second row, the left column says \u201cSquare the first term, x.\u201d The right column contains x squared minus blank. Above this is the general form a squared minus b squared. In the third row, the text on the left says \u201cSquare the last term, 8.\u201d The right column contains the expression x squared minus 8 squared. Above this is the general form a squared minus b squared. In the last row, the text in the left column says \u201cThe product is a difference of squares.\u201d The right column contains the expression x squared minus 64. Above this is the general form a squared minus b squared.\" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 314.98px;height: 15px\">Factor out the GCF (if any)<\/td>\r\n<td style=\"width: 266.987px;height: 15px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 314.98px;height: 15px\">Rewrite each term as a perfect square<\/td>\r\n<td style=\"width: 266.987px;height: 15px\">[latex]((6)^2 - (x-5)^2)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 314.98px;height: 15px\">Assigning values to \\(a\\) and \\(b\\)<\/td>\r\n<td style=\"width: 266.987px;height: 15px\">[latex]a = 6 , b =x-5[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 31px\">\r\n<td style=\"width: 314.98px;height: 31px\">Apply the difference of squares formula [latex]a^2 -b^2 = (a+b)(a-b)[\/latex]<\/td>\r\n<td style=\"width: 266.987px;height: 31px\">[latex](6+(x-5))(6-(x-5))[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 31px\">\r\n<td colspan=\"2\"><strong>Note the brackets around the [latex](x-5)[\/latex]. This is especially important in the second factor where we have a negative sign to take care of.\u00a0\u00a0<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 314.98px;height: 15px\">Rewrite to remove the inner brackets<\/td>\r\n<td style=\"width: 266.987px;height: 15px\">[latex](6+x-5)(6-x+5)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 314.98px;height: 15px\">Combine like terms<\/td>\r\n<td style=\"width: 266.987px;height: 15px\">[latex](1+x)(11-x)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 314.98px;height: 15px\">Hence,<\/td>\r\n<td style=\"width: 266.987px;height: 15px\">[latex]36-(x-5)^2 =\u00a0 (1+x)(11-x)[\/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-id1169596304022\" data-type=\"problem\">\r\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\r\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\r\n<p id=\"fs-id1169596302423\">Factor completely: [latex](x-7)^2 - 49[\/latex]<\/p>\r\n\r\n<\/div>\r\n<details open=\"open\"><summary>Show answer<\/summary>\r\n<div id=\"fs-id1169596303989\" data-type=\"solution\">[latex]x(x-14)[\/latex]<\/div>\r\n<\/details><\/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 8.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596304022\" data-type=\"problem\">\r\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\r\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\r\n<p id=\"fs-id1169596302423\">Factor completely: [latex]16 - (k+3)^2[\/latex]<\/p>\r\n\r\n<\/div>\r\n<details open=\"open\"><summary>Show answer<\/summary>\r\n<div id=\"fs-id1169596303989\" data-type=\"solution\">[latex](k+7)(1-k)[\/latex]<\/div>\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Practice Makes Perfect<\/h1>\r\n<p id=\"fs-id1168746325019\">In the following exercises, factorize using the difference of squares<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">1. \\({c}^{2}-25\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">2. [latex]m^2 -49[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">3. \\({b}^{2}-\\dfrac{36}{49}\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">4. \\({x}^2 - \\dfrac{9}{16}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">5. \\(64{j}^{2}-16\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">6. [latex]25k^2 - 36[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">7. \\(81{c}^{2}-25\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">8. [latex]121 k^2 - 16[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">9. \\(169-{q}^{2}\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">10. [latex]121 - b^2[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">11. \\(16-36{y}^{2}\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">12. [latex]25 - 9x^2[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">13. \\(49{w}^{2}-100{x}^{2}\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">14. [latex]81c^2 - 4d^2[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">15. \\({p}^{2}-\\dfrac{16}{25}{q}^{2}\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">16. \\({m}^{2}-\\dfrac{4}{9}{n}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">17. \\({x}^{2}{y}^{2}-81\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">18. [latex]a^2b^2 - 16[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">19. \\({r}^{2}{s}^{2}-\\dfrac{4}{49}\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">20. \\({u}^{2}{v}^{2}-\\dfrac{9}{25}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">21. [latex]7x^2-28y^2[\/latex]<\/td>\r\n<td style=\"width: 50%\">22. [latex]4x^2m-36y^2m[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">23. [latex]2x^4r - 72y^4r[\/latex]<\/td>\r\n<td style=\"width: 50%\">24. [latex]7x^4 - 343y^4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">25. [latex]25x^6-y^6[\/latex]<\/td>\r\n<td style=\"width: 50%\">26. [latex]16m^4-n^4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">27. [latex]16-(x-2)^2[\/latex]<\/td>\r\n<td style=\"width: 50%\">28. [latex]9y^2 - (y+9)^2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">29. [latex]0.25a^2-0.16b^2[\/latex]<\/td>\r\n<td style=\"width: 50%\">30. [latex]25 - (n+3)^2[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h1>Answers<\/h1>\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: 56.2194%;height: 14px\">1. \\(\\left(c-5\\right)\\left(c+5\\right)\\)<\/td>\r\n<td style=\"width: 43.7806%;height: 14px\">2. \\(\\left(m-7\\right)\\left(m+7\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 56.2194%;height: 14px\">3. \\(\\left(b+\\dfrac{6}{7}\\right)\\left(b-\\dfrac{6}{7}\\right)\\)<\/td>\r\n<td style=\"width: 43.7806%;height: 14px\">4. \\(\\left(x+\\dfrac{3}{4}\\right)\\left(x-\\dfrac{3}{4}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 56.2194%;height: 14px\">5. \\(\\left(8j+4\\right)\\left(8j-4\\right)\\)<\/td>\r\n<td style=\"width: 43.7806%;height: 14px\">6. \\(\\left(5k+6\\right)\\left(5k-6\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 56.2194%;height: 14px\">7. \\(\\left(9c+5\\right)\\left(9c-5\\right)\\)<\/td>\r\n<td style=\"width: 43.7806%;height: 14px\">8. \\(\\left(11k+4\\right)\\left(11k-4\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 56.2194%;height: 14px\">9. \\(\\left(13-q\\right)\\left(13+q\\right)\\)<\/td>\r\n<td style=\"width: 43.7806%;height: 14px\">10. \\(\\left(11-b\\right)\\left(11+b\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 56.2194%;height: 14px\">11. \\(\\left(4-6y\\right)\\left(4+6y\\right)\\)<\/td>\r\n<td style=\"width: 43.7806%;height: 14px\">12. \\(\\left(5-3x\\right)\\left(5+3x\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 56.2194%;height: 14px\">13. \\(\\left(7w+10x\\right)\\left(7w-10x\\right)\\)<\/td>\r\n<td style=\"width: 43.7806%;height: 14px\">14. \\(\\left(9c-2d\\right)\\left(9c+2d\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 56.2194%;height: 14px\">15. \\(\\left(p+\\dfrac{4}{5}q\\right)\\left(p-\\dfrac{4}{5}q\\right)\\)<\/td>\r\n<td style=\"width: 43.7806%;height: 14px\">16. \\(\\left(m+\\dfrac{2}{3}n\\right)\\left(m-\\dfrac{2}{3}n\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 56.2194%;height: 14px\">17. \\(\\left(xy-9\\right)\\left(xy+9\\right)\\)<\/td>\r\n<td style=\"width: 43.7806%;height: 14px\">18. \\(\\left(ab-4\\right)\\left(ab+4\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 56.2194%;height: 14px\">19. \\(\\left(rs-\\dfrac{2}{7}\\right)\\left(rs+\\dfrac{2}{7}\\right)\\)<\/td>\r\n<td style=\"width: 43.7806%;height: 14px\">20. \\(\\left(uv-\\dfrac{3}{5}\\right)\\left(uv+\\dfrac{3}{5}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 56.2194%\">21. [latex]7(x+2y)(x-2y)[\/latex]<\/td>\r\n<td style=\"width: 43.7806%\">22. [latex]4m(x+3y)(x-3y)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 56.2194%\">23. [latex]2r(x^2 + 6y^2)(x^2 - 6y^2)[\/latex]<\/td>\r\n<td style=\"width: 43.7806%\">24. [latex]7(x^2+7y^2)(x^2-7y^2)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 56.2194%\">25. [latex](5x^3 + y^3)(5x^3 - y^3)[\/latex]<\/td>\r\n<td style=\"width: 43.7806%\">26. [latex](4m^2+n^2)(2m+n)(2m-n)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 56.2194%\">27. [latex](x+2)(6-x)[\/latex]<\/td>\r\n<td style=\"width: 43.7806%\">28. [latex](4y+9)(2y-9)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 56.2194%\">29. [latex]0.01(5a+4b)(5a-4b) [\/latex] OR [latex](0.5a+0.4b)(0.5a-0.4b)[\/latex]<\/td>\r\n<td style=\"width: 43.7806%\">30. [latex](n+8)(2-n)[\/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>","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>Factor Binomials of the Form a<sup>2<\/sup>x<sup>2<\/sup> \u2013 b<sup>2<\/sup>y<sup>2<\/sup><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596391251\">Let us first review briefly what we learned in <a href=\"https:\/\/pressbooks.bccampus.ca\/math53\/chapter\/special-products\/\" target=\"_blank\" rel=\"noopener\">Chapter 6.3<\/a>:<\/p>\n<div id=\"fs-id1169596391023\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Product of Conjugates Pattern<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596391028\">If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4e1135b445e2550089a0e7fc0d9a1aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> are real numbers,<\/p>\n<p><span id=\"fs-id1169596367551\" data-type=\"media\" data-alt=\"This figure is divided into two sides. On the left side is the following formula: the product of a minus b and a plus b equals a squared minus b squared. On the right side is the same formula labeled: a minus b and a plus b are labeled \u201cconjugates\u201d, the a squared and b squared are labeled squares and the minus sign between the squares is labeled \u201cdifference\u201d. Therefore, the product of two conjugates is called a difference of squares.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/comp030\/wp-content\/uploads\/sites\/1048\/2021\/05\/CNX_ElemAlg_Figure_06_04_020_img_new.jpg\" alt=\"This figure is divided into two sides. On the left side is the following formula: the product of a minus b and a plus b equals a squared minus b squared. On the right side is the same formula labeled: a minus b and a plus b are labeled \u201cconjugates\u201d, the a squared and b squared are labeled squares and the minus sign between the squares is labeled \u201cdifference\u201d. Therefore, the product of two conjugates is called a difference of squares.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<p>The product is called a difference of squares.<\/p>\n<\/div>\n<h1>Factor the Difference of Squares<\/h1>\n<p id=\"fs-id1169596566014\">To be more specific, we are going to see how we can factorize the difference of <strong>two<\/strong> squares. From above, it is very clear that factors of a binomial of the type\u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2ac260b877ab9cb49262b6e150d587c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#45;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: 0px;\" \/> are always <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7b1f6a43c7d6c06df11deb5f865f7899_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;&#97;&#45;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -5px;\" \/>. Once we know what <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4e1135b445e2550089a0e7fc0d9a1aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/>\u00a0are, the factorization becomes very easy.<\/p>\n<\/div>\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-id1169596404708\" data-type=\"problem\">\n<p id=\"fs-id1169596404710\">Factor the difference of square: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f63bc71c08c6f40a26f6bdfb83b9b45e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#123;&#54;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1169596403359\" 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-id1169596403364\">First, we rewrite each term of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f63bc71c08c6f40a26f6bdfb83b9b45e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#123;&#54;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: 0px;\" \/> as a perfect square of an expression.<\/p>\n<table id=\"eip-id1172188052941\" 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 text in the left column says \u201cIt fits the pattern.\u201d The right column contains the product of x minus 8, in parentheses, and x plus 8, in parentheses. Above this is the general form a minus b, in parentheses, times a plus b, in parentheses. In the second row, the left column says \u201cSquare the first term, x.\u201d The right column contains x squared minus blank. Above this is the general form a squared minus b squared. In the third row, the text on the left says \u201cSquare the last term, 8.\u201d The right column contains the expression x squared minus 8 squared. Above this is the general form a squared minus b squared. In the last row, the text in the left column says \u201cThe product is a difference of squares.\u201d The right column contains the expression x squared minus 64. Above this is the general form a squared minus b squared.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 314.994px\">Rewrite each term as a perfect square<\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-2539\" src=\"https:\/\/pressbooks.bccampus.ca\/comp030\/wp-content\/uploads\/sites\/1048\/2022\/08\/Example-1-_pic1-1-300x75.png\" alt=\"\" width=\"300\" height=\"75\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 314.994px\">Treating <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;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7526b4b1bdd252ed6078521dfc29a03a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4e1135b445e2550089a0e7fc0d9a1aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-2542\" src=\"https:\/\/pressbooks.bccampus.ca\/comp030\/wp-content\/uploads\/sites\/1048\/2022\/08\/Example-1-_pic2-1-300x75.png\" alt=\"\" width=\"300\" height=\"75\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 314.994px\">Apply the difference of squares formula<\/td>\n<td style=\"width: 266.987px\"><span id=\"eip-id1172188052961\" data-type=\"media\" data-alt=\"The product of x minus 8 and x plus 8. Above this is the general form a minus b, in parentheses, times a plus b, in parentheses.\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-2544\" src=\"https:\/\/pressbooks.bccampus.ca\/comp030\/wp-content\/uploads\/sites\/1048\/2022\/08\/Example-1-_pic3-300x75.png\" alt=\"\" width=\"300\" height=\"75\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 314.994px\">Hence,<\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f63bc71c08c6f40a26f6bdfb83b9b45e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#123;&#54;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: 0px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c6b16c233af66db8eb4136f23151a9ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;&#40;&#120;&#43;&#56;&#41;&#40;&#120;&#45;&#56;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"127\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Difference of Squares<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596391028\">If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4e1135b445e2550089a0e7fc0d9a1aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> are real numbers, then<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2564 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/comp030\/wp-content\/uploads\/sites\/1048\/2022\/08\/diff_of_squares-300x75.png\" alt=\"difference of squares formula\" width=\"264\" height=\"66\" \/><\/p>\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-id1169596382320\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596376846\" data-type=\"exercise\">\n<div id=\"fs-id1169596376848\" data-type=\"problem\">\n<p>Factor:\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7206c37f3da1acc673177553eb127bee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#94;&#50;&#32;&#45;&#32;&#52;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"58\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1169596308784\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596569338\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-567d9bd010b61ae9f23146de100546bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#110;&#43;&#55;&#41;&#40;&#110;&#45;&#55;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\" \/><\/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 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596568300\" data-type=\"problem\">\n<p id=\"fs-id1169596568302\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-24ce6642aec37e5cab61094a8ec5d04d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"52\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596569446\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596569448\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-de8e6b240c391fafdeeab0a57cbbbb9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#119;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#119;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596568294\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596568297\" data-type=\"exercise\">\n<div id=\"fs-id1169596569446\" 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-id1169596361165\" data-type=\"problem\">\n<p>Factor completely: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d456e9833a493778805f38beb3941687_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"71\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596392529\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<\/div>\n<div id=\"fs-id1169596403359\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596403364\">We know that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f1ab39823ffad314a49c445f2f450355_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#109;&#94;&#50;&#32;&#61;&#32;&#40;&#50;&#109;&#41;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"102\" style=\"vertical-align: -5px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-06ca593917088dc2a447f62bd5b91b2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#49;&#32;&#61;&#32;&#57;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: 0px;\" \/><\/p>\n<table id=\"eip-id1172188052941\" 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 text in the left column says \u201cIt fits the pattern.\u201d The right column contains the product of x minus 8, in parentheses, and x plus 8, in parentheses. Above this is the general form a minus b, in parentheses, times a plus b, in parentheses. In the second row, the left column says \u201cSquare the first term, x.\u201d The right column contains x squared minus blank. Above this is the general form a squared minus b squared. In the third row, the text on the left says \u201cSquare the last term, 8.\u201d The right column contains the expression x squared minus 8 squared. Above this is the general form a squared minus b squared. In the last row, the text in the left column says \u201cThe product is a difference of squares.\u201d The right column contains the expression x squared minus 64. Above this is the general form a squared minus b squared.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 314.994px\">Rewrite each term as a perfect square<\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7d15ba36174abff3217b04ccf015452c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#50;&#109;&#41;&#94;&#50;&#32;&#45;&#32;&#57;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"83\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 314.994px\">Treating <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b0fcf1acfd4de658e8e5b2d9689d22a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"24\" style=\"vertical-align: 0px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-169193ff8b4fc5625a37c03183cf5bf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4e1135b445e2550089a0e7fc0d9a1aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-515e1acd7ec6b82fde4013ba9c9e1cc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#61;&#32;&#50;&#109;&#32;&#44;&#32;&#98;&#32;&#61;&#32;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"106\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 314.994px\">Apply the difference of squares formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-543e1cc91bcbc6e838e8539fba970789_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#50;&#32;&#45;&#98;&#94;&#50;&#32;&#61;&#32;&#40;&#97;&#43;&#98;&#41;&#40;&#97;&#45;&#98;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"182\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-09a164a2a4c8502a4c6fcd02c1ef1b9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#50;&#109;&#43;&#57;&#41;&#40;&#50;&#109;&#45;&#57;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 314.994px\">Hence,<\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d456e9833a493778805f38beb3941687_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"71\" style=\"vertical-align: 0px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5c537f412c7f209e07288ebf53ce143e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;&#40;&#50;&#109;&#43;&#57;&#41;&#40;&#50;&#109;&#45;&#57;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"155\" style=\"vertical-align: -5px;\" \/><\/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-id1169596566475\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596566479\" data-type=\"exercise\">\n<div id=\"fs-id1169596555445\" data-type=\"problem\">\n<p id=\"fs-id1169596555447\">Factor completely: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2043614b2130126f76decae42149753f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"75\" style=\"vertical-align: 0px;\" \/> .<\/p>\n<\/div>\n<div id=\"fs-id1169596308819\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596308821\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e7d0dd8952de7dd86cafb593bb774551_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#120;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#120;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -5px;\" \/><\/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 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596366001\" data-type=\"problem\">\n<p id=\"fs-id1169596381369\">Factor completely: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d6ef0cd1bd8cdd6a4a57131033164114_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#125;&#123;&#49;&#50;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"86\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596404475\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596404477\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ab187087bcd3b5ca8e9e113b65b939ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#120;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#120;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"174\" style=\"vertical-align: -17px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>Now we\u2019ll factor a similar binomial that has two variables.<\/p>\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-id1169596276239\" data-type=\"problem\">\n<div id=\"fs-id1169596361165\" data-type=\"problem\">\n<p>Factor completely: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-060453a1e45232fb3ca599700bbc9d7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#123;&#121;&#125;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596392529\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<\/div>\n<div id=\"fs-id1169596403359\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596403364\">We know that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4509963e4baf669483f998dcbdab3ff6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#61;&#53;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: 0px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2b29288448f049913ca8e7a536cd6a5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#94;&#50;&#32;&#61;&#32;&#40;&#120;&#41;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"72\" style=\"vertical-align: -5px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7555a018d85fc0367999da3dd341d3eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#50;&#32;&#61;&#32;&#40;&#121;&#41;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"71\" style=\"vertical-align: -5px;\" \/><\/p>\n<table id=\"eip-id1172188052941\" 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 text in the left column says \u201cIt fits the pattern.\u201d The right column contains the product of x minus 8, in parentheses, and x plus 8, in parentheses. Above this is the general form a minus b, in parentheses, times a plus b, in parentheses. In the second row, the left column says \u201cSquare the first term, x.\u201d The right column contains x squared minus blank. Above this is the general form a squared minus b squared. In the third row, the text on the left says \u201cSquare the last term, 8.\u201d The right column contains the expression x squared minus 8 squared. Above this is the general form a squared minus b squared. In the last row, the text in the left column says \u201cThe product is a difference of squares.\u201d The right column contains the expression x squared minus 64. Above this is the general form a squared minus b squared.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 314.994px\">Rewrite each term as a perfect square<\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-eb66d0eefd465494d67fb3cc9dfb38bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#53;&#120;&#41;&#94;&#50;&#32;&#45;&#32;&#40;&#121;&#41;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"91\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 314.994px\">Assigning values to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4e1135b445e2550089a0e7fc0d9a1aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-74065def11d4898b4b9845843a4494d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#61;&#32;&#53;&#120;&#32;&#44;&#32;&#98;&#32;&#61;&#32;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 314.994px\">Apply the difference of squares formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-543e1cc91bcbc6e838e8539fba970789_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#50;&#32;&#45;&#98;&#94;&#50;&#32;&#61;&#32;&#40;&#97;&#43;&#98;&#41;&#40;&#97;&#45;&#98;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"182\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7a13a6d92de39baebdc6bb9f5bc6a32c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#53;&#120;&#43;&#121;&#41;&#40;&#53;&#120;&#45;&#121;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 314.994px\">Hence,<\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1cdb74239b45f6e8f8080deb40b4f1cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#120;&#94;&#50;&#32;&#45;&#32;&#121;&#94;&#50;&#32;&#61;&#32;&#40;&#53;&#120;&#43;&#121;&#41;&#40;&#53;&#120;&#45;&#121;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"225\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596574039\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596574042\" data-type=\"exercise\">\n<div id=\"fs-id1169596574044\" data-type=\"problem\">\n<p id=\"fs-id1169596574046\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e4b229643aaf38c0ccd375246c3b0e83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#57;&#123;&#121;&#125;&#94;&#50;&#45;&#49;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"91\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596391449\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596391451\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a4778889bca82b5e8112105b16f761c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#121;&#43;&#52;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#121;&#45;&#52;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -5px;\" \/><\/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 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596393084\" data-type=\"problem\">\n<p id=\"fs-id1169596393086\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-34c6c2ac5486bea7f0a491aaa1933904_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#49;&#123;&#109;&#125;&#94;&#50;&#45;&#52;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"90\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596455633\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596455635\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1255d9b303b596f9808c15454697fa92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#109;&#43;&#50;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#109;&#45;&#50;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"160\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596392876\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596392880\" data-type=\"exercise\">\n<div id=\"fs-id1169596555078\" 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-id1169596360904\" data-type=\"problem\">\n<div id=\"fs-id1169596361165\" data-type=\"problem\">\n<p>Factor completely: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9dacfb2ef7b60e9ce6f14efb2deb399_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#50;&#32;&#45;&#32;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596392529\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<\/div>\n<div id=\"fs-id1169596403359\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596403364\">We know that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4509963e4baf669483f998dcbdab3ff6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#61;&#53;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: 0px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2b29288448f049913ca8e7a536cd6a5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#94;&#50;&#32;&#61;&#32;&#40;&#120;&#41;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"72\" style=\"vertical-align: -5px;\" \/> , <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7555a018d85fc0367999da3dd341d3eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#50;&#32;&#61;&#32;&#40;&#121;&#41;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"71\" style=\"vertical-align: -5px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7c40613b30c26494d58cdb228298585a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;&#32;&#61;&#32;&#54;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: 0px;\" \/><\/p>\n<table id=\"eip-id1172188052941\" 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 text in the left column says \u201cIt fits the pattern.\u201d The right column contains the product of x minus 8, in parentheses, and x plus 8, in parentheses. Above this is the general form a minus b, in parentheses, times a plus b, in parentheses. In the second row, the left column says \u201cSquare the first term, x.\u201d The right column contains x squared minus blank. Above this is the general form a squared minus b squared. In the third row, the text on the left says \u201cSquare the last term, 8.\u201d The right column contains the expression x squared minus 8 squared. Above this is the general form a squared minus b squared. In the last row, the text in the left column says \u201cThe product is a difference of squares.\u201d The right column contains the expression x squared minus 64. Above this is the general form a squared minus b squared.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 314.994px\">Rewrite each term as a perfect square<\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d2cc74f66572c065c45b45a0624554d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#53;&#120;&#121;&#41;&#94;&#50;&#32;&#45;&#32;&#40;&#54;&#41;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"100\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 314.994px\">Assigning values to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4e1135b445e2550089a0e7fc0d9a1aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-510f3beac076beebdf7919f92cb99a64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#61;&#32;&#53;&#120;&#121;&#32;&#44;&#32;&#98;&#32;&#61;&#32;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 314.994px\">Apply the difference of squares formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-543e1cc91bcbc6e838e8539fba970789_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#50;&#32;&#45;&#98;&#94;&#50;&#32;&#61;&#32;&#40;&#97;&#43;&#98;&#41;&#40;&#97;&#45;&#98;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"182\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-96fd412bac3a69b2f202f35c0aeb01ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#53;&#120;&#121;&#43;&#54;&#41;&#40;&#53;&#120;&#121;&#45;&#54;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"144\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 314.994px\">Hence,<\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5a14307ae56b864926f3ecf88005aa71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#120;&#94;&#50;&#121;&#94;&#50;&#32;&#45;&#32;&#51;&#54;&#32;&#61;&#32;&#40;&#53;&#120;&#121;&#43;&#54;&#41;&#40;&#53;&#120;&#121;&#45;&#54;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"260\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596303932\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596303936\" data-type=\"exercise\">\n<div id=\"fs-id1169596303938\" data-type=\"problem\">\n<p id=\"fs-id1169596303940\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-09d38c3a3d95fcd7c585b1ffae431327_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596566590\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596566592\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-10f815fbd7c544cebff2c44b315b2647_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#121;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#121;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -5px;\" \/><\/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 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596574406\" data-type=\"problem\">\n<p id=\"fs-id1169596574408\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ac0ef9afa2ff8e6236fb957afac6f048_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"71\" style=\"vertical-align: 0px;\" \/> .<\/p>\n<\/div>\n<div id=\"fs-id1169596366993\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596366995\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c6e08e4da3ae288b4d1488bccd13e939_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#98;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#98;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>Let us now try to factor a binomial where it is not apparent that we can use the Difference of Squares formula right away.<\/p>\n<div id=\"fs-id1169596574400\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596574404\" data-type=\"exercise\">\n<div id=\"fs-id1169596366993\" 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-id1169596569315\" data-type=\"problem\">\n<p id=\"fs-id1169596569317\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-48df1ef1242186197856f4656d899d15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#97;&#94;&#50;&#32;&#45;&#32;&#50;&#55;&#98;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"81\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<p id=\"fs-id1169596403364\">We know that\u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e2a09a478ed643560e97ce8419e17f33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#50;&#32;&#61;&#32;&#40;&#97;&#41;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"71\" style=\"vertical-align: -5px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8a5bca5a38087cdf4e03f853b44f45a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#94;&#50;&#32;&#61;&#32;&#40;&#98;&#41;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"68\" style=\"vertical-align: -5px;\" \/> but neither 3 nor 27 is a perfect square. In a question like this check whether the numbers have a GCF other than 1. In this case, the GCF of 3 and 27 is 3.\u00a0 Now apply your knowledge of factoring out the GCF and check if you can factor the binomial any further:<\/p>\n<table id=\"eip-id1172188052941\" 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 text in the left column says \u201cIt fits the pattern.\u201d The right column contains the product of x minus 8, in parentheses, and x plus 8, in parentheses. Above this is the general form a minus b, in parentheses, times a plus b, in parentheses. In the second row, the left column says \u201cSquare the first term, x.\u201d The right column contains x squared minus blank. Above this is the general form a squared minus b squared. In the third row, the text on the left says \u201cSquare the last term, 8.\u201d The right column contains the expression x squared minus 8 squared. Above this is the general form a squared minus b squared. In the last row, the text in the left column says \u201cThe product is a difference of squares.\u201d The right column contains the expression x squared minus 64. Above this is the general form a squared minus b squared.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 314.994px\">Factor out the GCF<\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a28990626bc55cc9c318fb017e32a18c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#40;&#97;&#94;&#50;&#32;&#45;&#57;&#98;&#94;&#50;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"85\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 314.994px\">Rewrite each term as a perfect square<\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-63bc33116d75da652b304928d1b1a637_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#40;&#40;&#97;&#41;&#94;&#50;&#32;&#45;&#32;&#40;&#51;&#98;&#41;&#94;&#50;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"112\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 314.994px\">Assigning values to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4e1135b445e2550089a0e7fc0d9a1aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ecade26c60e05d908cb9442ac4073cc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#61;&#32;&#97;&#32;&#44;&#32;&#98;&#32;&#61;&#32;&#51;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"99\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 314.994px\">Apply the difference of squares formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-543e1cc91bcbc6e838e8539fba970789_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#50;&#32;&#45;&#98;&#94;&#50;&#32;&#61;&#32;&#40;&#97;&#43;&#98;&#41;&#40;&#97;&#45;&#98;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"182\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fb3431e6f3beba23b4e9f9b87b9a8bcc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#40;&#97;&#43;&#51;&#98;&#41;&#40;&#97;&#45;&#51;&#98;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"131\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 314.994px\">Hence,<\/td>\n<td style=\"width: 266.987px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5964ba520839aa3e724b6b9b8f8b702d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#97;&#94;&#50;&#32;&#45;&#32;&#50;&#55;&#98;&#94;&#50;&#32;&#61;&#32;&#51;&#40;&#97;&#43;&#51;&#98;&#41;&#40;&#97;&#45;&#51;&#98;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"235\" style=\"vertical-align: -5px;\" \/><\/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-id1169596302415\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596302419\" data-type=\"exercise\">\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\n<p id=\"fs-id1169596302423\">Factor completely: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-300cb907a7665a17af095a943f25ea1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;&#120;&#94;&#50;&#45;&#57;&#121;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<div id=\"fs-id1169596303989\" data-type=\"solution\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cbd8e81cfd74a054448d25ed2bd854ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#40;&#50;&#120;&#43;&#121;&#41;&#40;&#50;&#120;&#45;&#121;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/details>\n<p>&nbsp;<\/p>\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 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596304022\" data-type=\"problem\">\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\n<p id=\"fs-id1169596302423\">Factor completely: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-73bff83d9d7fc8b7507aa9c0743dba78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#54;&#120;&#94;&#50;&#45;&#48;&#46;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"85\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<div id=\"fs-id1169596303989\" data-type=\"solution\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b46ef85a4524768c208718ccaed0a079_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#57;&#40;&#50;&#120;&#43;&#49;&#41;&#40;&#50;&#120;&#45;&#49;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596574400\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596574404\" data-type=\"exercise\">\n<div id=\"fs-id1169596366993\" 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-id1169596569315\" data-type=\"problem\">\n<p id=\"fs-id1169596569317\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4d85ba208ec8d4a8ad6cd9e790698e6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#94;&#52;&#32;&#45;&#32;&#121;&#94;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<p id=\"fs-id1169596403364\">We know that\u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-baeeda35e9b655a825fc8788bda416dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#94;&#52;&#32;&#61;&#32;&#40;&#120;&#94;&#50;&#41;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"80\" style=\"vertical-align: -5px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1d8ea8738db308c8f671864c279abdd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#54;&#32;&#61;&#32;&#40;&#121;&#94;&#51;&#41;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"79\" style=\"vertical-align: -5px;\" \/><\/p>\n<table id=\"eip-id1172188052941\" class=\"unnumbered unstyled\" style=\"height: 91px\" summary=\"This figure 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 fits the pattern.\u201d The right column contains the product of x minus 8, in parentheses, and x plus 8, in parentheses. Above this is the general form a minus b, in parentheses, times a plus b, in parentheses. In the second row, the left column says \u201cSquare the first term, x.\u201d The right column contains x squared minus blank. Above this is the general form a squared minus b squared. In the third row, the text on the left says \u201cSquare the last term, 8.\u201d The right column contains the expression x squared minus 8 squared. Above this is the general form a squared minus b squared. In the last row, the text in the left column says \u201cThe product is a difference of squares.\u201d The right column contains the expression x squared minus 64. Above this is the general form a squared minus b squared.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 15px\">\n<td style=\"width: 314.98px;height: 15px\">Factor out the GCF (if any)<\/td>\n<td style=\"width: 266.987px;height: 15px\"><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 314.98px;height: 15px\">Rewrite each term as a perfect square<\/td>\n<td style=\"width: 266.987px;height: 15px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0f0af3229b87ba7427799e4d1b8d0326_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#40;&#120;&#94;&#50;&#41;&#94;&#50;&#32;&#45;&#32;&#40;&#121;&#94;&#51;&#41;&#94;&#50;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"111\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 314.98px;height: 15px\">Assigning values to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4e1135b445e2550089a0e7fc0d9a1aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 266.987px;height: 15px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-26a7d4bf79ee913f4a91ff9886e659fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#61;&#32;&#120;&#94;&#50;&#32;&#44;&#32;&#98;&#32;&#61;&#32;&#121;&#94;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 31px\">\n<td style=\"width: 314.98px;height: 31px\">Apply the difference of squares formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-543e1cc91bcbc6e838e8539fba970789_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#50;&#32;&#45;&#98;&#94;&#50;&#32;&#61;&#32;&#40;&#97;&#43;&#98;&#41;&#40;&#97;&#45;&#98;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"182\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 266.987px;height: 31px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-360f570a37582f1c320cd5c233e0052e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#120;&#94;&#50;&#43;&#121;&#94;&#51;&#41;&#40;&#120;&#94;&#50;&#45;&#121;&#94;&#51;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"139\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 314.98px;height: 15px\">Hence,<\/td>\n<td style=\"width: 266.987px;height: 15px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4ca25c4e7fa138a355e3b85e1d20cd7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#94;&#52;&#32;&#45;&#32;&#121;&#94;&#54;&#32;&#61;&#32;&#32;&#40;&#120;&#94;&#50;&#43;&#121;&#94;&#51;&#41;&#40;&#120;&#94;&#50;&#45;&#121;&#94;&#51;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"220\" style=\"vertical-align: -5px;\" \/><\/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-id1169596302415\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596302419\" data-type=\"exercise\">\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\n<p id=\"fs-id1169596302423\">Factor completely: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6586560bdc03c27cd838196c7c2ce12a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#94;&#52;&#32;&#45;&#32;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<div id=\"fs-id1169596303989\" data-type=\"solution\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f93836fbbe0f8646cebbafd79dd8d955_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#120;&#94;&#50;&#43;&#51;&#41;&#40;&#120;&#94;&#50;&#45;&#51;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"123\" style=\"vertical-align: -5px;\" \/><\/div>\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 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596302415\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596302419\" data-type=\"exercise\">\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\n<p id=\"fs-id1169596302423\">Factor completely: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-22f654977f4e420a2cbb8519b429c212_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#109;&#94;&#52;&#110;&#94;&#50;&#32;&#45;&#32;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"90\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<div id=\"fs-id1169596303989\" data-type=\"solution\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-433a77c446a38c1dc9a52113ac7e0d73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#40;&#109;&#94;&#50;&#110;&#43;&#53;&#41;&#40;&#109;&#94;&#50;&#110;&#45;&#53;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"165\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Can you factor Sum of Squares?<\/p>\n<\/header>\n<div class=\"textbox__content\">Note that, except for a common factor, a sum of squares or a binomial of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f034ae2fb01162633db19165e51943ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#50;&#32;&#43;&#32;&#98;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"54\" style=\"vertical-align: -2px;\" \/> is not factorable over the set of real numbers.<\/div>\n<\/div>\n<div id=\"fs-id1169596574400\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596574404\" data-type=\"exercise\">\n<div id=\"fs-id1169596366993\" data-type=\"solution\">\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-id1169596569315\" data-type=\"problem\">\n<p id=\"fs-id1169596569317\">Factor completely: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d2457824ffdf4997e377c26c7bf06b6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#94;&#52;&#32;&#45;&#32;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<p id=\"fs-id1169596403364\">We know that\u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-baeeda35e9b655a825fc8788bda416dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#94;&#52;&#32;&#61;&#32;&#40;&#120;&#94;&#50;&#41;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"80\" style=\"vertical-align: -5px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3b59542a34a68831c80eee4dfac7f638_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#32;&#61;&#32;&#40;&#52;&#41;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"70\" style=\"vertical-align: -5px;\" \/><\/p>\n<table id=\"eip-id1172188052941\" class=\"unnumbered unstyled\" style=\"height: 91px\" summary=\"This figure 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 fits the pattern.\u201d The right column contains the product of x minus 8, in parentheses, and x plus 8, in parentheses. Above this is the general form a minus b, in parentheses, times a plus b, in parentheses. In the second row, the left column says \u201cSquare the first term, x.\u201d The right column contains x squared minus blank. Above this is the general form a squared minus b squared. In the third row, the text on the left says \u201cSquare the last term, 8.\u201d The right column contains the expression x squared minus 8 squared. Above this is the general form a squared minus b squared. In the last row, the text in the left column says \u201cThe product is a difference of squares.\u201d The right column contains the expression x squared minus 64. Above this is the general form a squared minus b squared.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 15px\">\n<td style=\"width: 314.98px;height: 15px\">Factor out the GCF (if any)<\/td>\n<td style=\"width: 266.987px;height: 15px\"><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 314.98px;height: 15px\">Rewrite each term as a perfect square<\/td>\n<td style=\"width: 266.987px;height: 15px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e9078d5c3c2a23f3c664eecf6da79322_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#40;&#120;&#94;&#50;&#41;&#94;&#50;&#32;&#45;&#32;&#40;&#52;&#41;&#94;&#50;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"103\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 314.98px;height: 15px\">Assigning values to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4e1135b445e2550089a0e7fc0d9a1aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 266.987px;height: 15px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-27dd739d109d0ea669cf1eb07a18391b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#61;&#32;&#120;&#94;&#50;&#32;&#44;&#32;&#98;&#32;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"99\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 31px\">\n<td style=\"width: 314.98px;height: 31px\">Apply the difference of squares formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-543e1cc91bcbc6e838e8539fba970789_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#50;&#32;&#45;&#98;&#94;&#50;&#32;&#61;&#32;&#40;&#97;&#43;&#98;&#41;&#40;&#97;&#45;&#98;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"182\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 266.987px;height: 31px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a29ca785a9459ea3efb6a9bf694ef0e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#120;&#94;&#50;&#43;&#52;&#41;&#40;&#120;&#94;&#50;&#45;&#52;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"123\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 31px\">\n<td colspan=\"2\"><strong>So far, this question is not much different from the previous examples but note that this factorization is incomplete. Why? Because the second factor <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b7108a813d4d85af221029f9fd8772fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#120;&#94;&#50;&#45;&#52;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"60\" style=\"vertical-align: -5px;\" \/> can also be rewritten as a difference of squares. The first factor <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9c519f146512e26668308f551a8d2c82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#120;&#94;&#50;&#43;&#52;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"60\" style=\"vertical-align: -5px;\" \/> is a sum of squares and cannot be factored further over the set of real numbers.\u00a0<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 314.98px;height: 15px\">Rewrite each term of the second factor as a perfect square<\/td>\n<td style=\"width: 266.987px;height: 15px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d59d7ec600efd5b00034115b8d94027e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#120;&#94;&#50;&#43;&#52;&#41;&#40;&#40;&#120;&#41;&#94;&#50;&#32;&#45;&#32;&#40;&#50;&#41;&#94;&#50;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"158\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 314.98px;height: 15px\">Assigning values to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4e1135b445e2550089a0e7fc0d9a1aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 266.987px;height: 15px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4cf890f020a9a140de37ed9f3fbf7272_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#61;&#32;&#120;&#32;&#44;&#32;&#98;&#32;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 31px\">\n<td style=\"width: 314.98px;height: 31px\">Apply the difference of squares formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-543e1cc91bcbc6e838e8539fba970789_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#50;&#32;&#45;&#98;&#94;&#50;&#32;&#61;&#32;&#40;&#97;&#43;&#98;&#41;&#40;&#97;&#45;&#98;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"182\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 266.987px;height: 31px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-57db35ef56b93f83e8c5a7dec3ab8b1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#120;&#94;&#50;&#43;&#52;&#41;&#40;&#120;&#43;&#50;&#41;&#40;&#120;&#45;&#50;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"169\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 314.98px;height: 15px\">Hence,<\/td>\n<td style=\"width: 266.987px;height: 15px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9b4836eb530753aa5685abb7a1d35afb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#94;&#52;&#32;&#45;&#32;&#49;&#54;&#32;&#61;&#32;&#32;&#40;&#120;&#94;&#50;&#43;&#52;&#41;&#40;&#120;&#43;&#50;&#41;&#40;&#120;&#45;&#50;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"251\" style=\"vertical-align: -5px;\" \/><\/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<div id=\"fs-id1169596304022\" data-type=\"problem\">\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\n<p id=\"fs-id1169596302423\">Factor completely: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8a59b7b0e2f6fbf7e063c42e3327b0e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#52;&#32;&#45;&#32;&#56;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<div id=\"fs-id1169596303989\" data-type=\"solution\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ee40117fa72debd676c0727038fde158_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#121;&#94;&#50;&#32;&#43;&#57;&#41;&#40;&#121;&#43;&#51;&#41;&#40;&#121;&#45;&#51;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"167\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/details>\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 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596304022\" data-type=\"problem\">\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\n<p id=\"fs-id1169596302423\">Factor completely: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c3ae63a1865cbfdc31c396bca557fb76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#112;&#94;&#52;&#32;&#45;&#32;&#56;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<div id=\"fs-id1169596303989\" data-type=\"solution\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bb1beb6e73fe8cba5efb4f7dabd80765_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#40;&#112;&#94;&#50;&#32;&#43;&#32;&#52;&#41;&#40;&#112;&#43;&#50;&#41;&#40;&#112;&#45;&#50;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"176\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596574400\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596574400\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596574404\" data-type=\"exercise\">\n<div id=\"fs-id1169596366993\" 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-id1169596569315\" data-type=\"problem\">\n<p id=\"fs-id1169596569317\">Factor completely: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e622dbe41a897c5575152ca4a57bef68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;&#45;&#40;&#120;&#45;&#53;&#41;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"101\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<p id=\"fs-id1169596403364\">We can apply the difference of squares formula not only on monomials that are perfect squares but also on any polynomial that is a perfect square. In this example, we know that\u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8fbe2d83bf5d3686d10ab18e2f871034_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;&#32;&#61;&#32;&#40;&#54;&#41;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"71\" style=\"vertical-align: -5px;\" \/> and the second term is already in the form of a perfect square.<\/p>\n<table id=\"eip-id1172188052941\" class=\"unnumbered unstyled\" style=\"height: 91px\" summary=\"This figure 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 fits the pattern.\u201d The right column contains the product of x minus 8, in parentheses, and x plus 8, in parentheses. Above this is the general form a minus b, in parentheses, times a plus b, in parentheses. In the second row, the left column says \u201cSquare the first term, x.\u201d The right column contains x squared minus blank. Above this is the general form a squared minus b squared. In the third row, the text on the left says \u201cSquare the last term, 8.\u201d The right column contains the expression x squared minus 8 squared. Above this is the general form a squared minus b squared. In the last row, the text in the left column says \u201cThe product is a difference of squares.\u201d The right column contains the expression x squared minus 64. Above this is the general form a squared minus b squared.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 15px\">\n<td style=\"width: 314.98px;height: 15px\">Factor out the GCF (if any)<\/td>\n<td style=\"width: 266.987px;height: 15px\"><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 314.98px;height: 15px\">Rewrite each term as a perfect square<\/td>\n<td style=\"width: 266.987px;height: 15px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-405aabd7a490c1775a883e4bec9b622e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#40;&#54;&#41;&#94;&#50;&#32;&#45;&#32;&#40;&#120;&#45;&#53;&#41;&#94;&#50;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"126\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 314.98px;height: 15px\">Assigning values to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4e1135b445e2550089a0e7fc0d9a1aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 266.987px;height: 15px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7e01d1eaefb58238e5fc820e48eb28b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#61;&#32;&#54;&#32;&#44;&#32;&#98;&#32;&#61;&#120;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"121\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 31px\">\n<td style=\"width: 314.98px;height: 31px\">Apply the difference of squares formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-543e1cc91bcbc6e838e8539fba970789_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#50;&#32;&#45;&#98;&#94;&#50;&#32;&#61;&#32;&#40;&#97;&#43;&#98;&#41;&#40;&#97;&#45;&#98;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"182\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 266.987px;height: 31px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-321dc6f37c27d72b064eb5688d8409d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#54;&#43;&#40;&#120;&#45;&#53;&#41;&#41;&#40;&#54;&#45;&#40;&#120;&#45;&#53;&#41;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"196\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 31px\">\n<td colspan=\"2\"><strong>Note the brackets around the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-38b154480d76a3dbb86394a498ddb4d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#120;&#45;&#53;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"53\" style=\"vertical-align: -5px;\" \/>. This is especially important in the second factor where we have a negative sign to take care of.\u00a0\u00a0<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 314.98px;height: 15px\">Rewrite to remove the inner brackets<\/td>\n<td style=\"width: 266.987px;height: 15px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1e2d776ea7ebb5ebea5f98f88b6f96d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#54;&#43;&#120;&#45;&#53;&#41;&#40;&#54;&#45;&#120;&#43;&#53;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"168\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 314.98px;height: 15px\">Combine like terms<\/td>\n<td style=\"width: 266.987px;height: 15px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bf74406aebbf2d26b5d6de9f9cc54e67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#49;&#43;&#120;&#41;&#40;&#49;&#49;&#45;&#120;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 314.98px;height: 15px\">Hence,<\/td>\n<td style=\"width: 266.987px;height: 15px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b7b3a2eb0f2726e6391933a093d3c3f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;&#45;&#40;&#120;&#45;&#53;&#41;&#94;&#50;&#32;&#61;&#32;&#32;&#40;&#49;&#43;&#120;&#41;&#40;&#49;&#49;&#45;&#120;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"242\" style=\"vertical-align: -5px;\" \/><\/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-id1169596304022\" data-type=\"problem\">\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\n<p id=\"fs-id1169596302423\">Factor completely: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f7934f146264c2e141fc010181bcf9aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#120;&#45;&#55;&#41;&#94;&#50;&#32;&#45;&#32;&#52;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"101\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/div>\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<div id=\"fs-id1169596303989\" data-type=\"solution\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3dc4f6de28f0b4e437d417c4ac2165bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#40;&#120;&#45;&#49;&#52;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"73\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/details>\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 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596304022\" data-type=\"problem\">\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\n<div id=\"fs-id1169596302421\" data-type=\"problem\">\n<p id=\"fs-id1169596302423\">Factor completely: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e8e81ea88c8dc93db0fdeb1efd684001_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#32;&#45;&#32;&#40;&#107;&#43;&#51;&#41;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"100\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/div>\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<div id=\"fs-id1169596303989\" data-type=\"solution\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4e9254e1eb32f7eea3a318f3d5cf239d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#107;&#43;&#55;&#41;&#40;&#49;&#45;&#107;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Practice Makes Perfect<\/h1>\n<p id=\"fs-id1168746325019\">In the following exercises, factorize using the difference of squares<\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\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-e73d4bc6c2f3e89f7b242b0d23d31ec1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: 0px;\" \/><\/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-1538c83a1e8ffab01dadda734b131b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#94;&#50;&#32;&#45;&#52;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"63\" style=\"vertical-align: 0px;\" \/><\/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-4fccac275d309dc371f42e1c3df02801_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#54;&#125;&#123;&#52;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"57\" style=\"vertical-align: -12px;\" \/><\/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-9261ec792ec987eb1f2401429f6ac85a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#50;&#32;&#45;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"59\" style=\"vertical-align: -12px;\" \/><\/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-5b62200d7e671131626693600cce16ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#52;&#123;&#106;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/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-f2beb12404ab64a167171b8d20109a20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#107;&#94;&#50;&#32;&#45;&#32;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"75\" style=\"vertical-align: 0px;\" \/><\/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-407e7c1c487be87b658cc6df19b8623e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#49;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"72\" style=\"vertical-align: 0px;\" \/><\/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-73fc520609266236696fb5f2ccd8f3d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#49;&#32;&#107;&#94;&#50;&#32;&#45;&#32;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"83\" style=\"vertical-align: 0px;\" \/><\/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-e963f49651b3376b2af44d1b3869d8b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#57;&#45;&#123;&#113;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"63\" style=\"vertical-align: -4px;\" \/><\/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-4b07217ff1890d3ed21d63be74c743b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#49;&#32;&#45;&#32;&#98;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"62\" style=\"vertical-align: 0px;\" \/><\/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-04062558df58e0323dafd197139dab40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#45;&#51;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -4px;\" \/><\/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-256bce3e1b48db738c67f0bb06676832_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#32;&#45;&#32;&#57;&#120;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"65\" style=\"vertical-align: 0px;\" \/><\/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-1882c62c128df09e4ff3138a33f52c52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#57;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#48;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"104\" style=\"vertical-align: 0px;\" \/><\/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-8eff5400436b71d02a1e26156308b9a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#49;&#99;&#94;&#50;&#32;&#45;&#32;&#52;&#100;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"80\" style=\"vertical-align: 0px;\" \/><\/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-ae618dd6bb9ff8eef78bd1ef8ed309d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#54;&#125;&#123;&#50;&#53;&#125;&#123;&#113;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"76\" style=\"vertical-align: -12px;\" \/><\/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-4ea1f8a177f63bcc089bf172bfb4189f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#57;&#125;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"76\" style=\"vertical-align: -12px;\" \/><\/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-c2ab7ee8666eed655d9f345c62cf13ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/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-3f9308fded21e3011c5a701bd7e12eeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#50;&#98;&#94;&#50;&#32;&#45;&#32;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"72\" style=\"vertical-align: 0px;\" \/><\/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-3ecb5dba05194d8eb572e560db9e2bfe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#52;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"74\" style=\"vertical-align: -12px;\" \/><\/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-3af47cba51a721b65012d1a082bbe0f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"76\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-120f9f875136ed36bae97e242132866b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#94;&#50;&#45;&#50;&#56;&#121;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%\">22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fe4c557fe0be5f9d565519c9cc2b00fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#94;&#50;&#109;&#45;&#51;&#54;&#121;&#94;&#50;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"114\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-39f9e63f7ebc8170538ad0e511543f10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#94;&#52;&#114;&#32;&#45;&#32;&#55;&#50;&#121;&#94;&#52;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"100\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%\">24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-099410c18e90713f6742b6ce8845c309_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#94;&#52;&#32;&#45;&#32;&#51;&#52;&#51;&#121;&#94;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b423dc6eb43693608efbc43ca80ba039_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#120;&#94;&#54;&#45;&#121;&#94;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6a8d934b52702191671f594e5aac9a39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#109;&#94;&#52;&#45;&#110;&#94;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"80\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-865ea40d335ebd36b350353f73871240_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#45;&#40;&#120;&#45;&#50;&#41;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"100\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%\">28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1da973a073dd88967f96d8ab89d8feaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#121;&#94;&#50;&#32;&#45;&#32;&#40;&#121;&#43;&#57;&#41;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"108\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f37d31b925290f124f6888444f808e93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#50;&#53;&#97;&#94;&#50;&#45;&#48;&#46;&#49;&#54;&#98;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"117\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%\">30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-040b00ae72c89b3d7f39f2c8896efb36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#32;&#45;&#32;&#40;&#110;&#43;&#51;&#41;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"102\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse;width: 100%;height: 140px\">\n<tbody>\n<tr style=\"height: 14px\">\n<td style=\"width: 56.2194%;height: 14px\">1. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6ebf2fa601ac5e1c342b8b85abf977f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#99;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#99;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 43.7806%;height: 14px\">2. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-33862e3fded47e7671333dc52a0a859b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"121\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 56.2194%;height: 14px\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5eb3ce5b9885a3177b103ba21dcc6369_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"133\" style=\"vertical-align: -17px;\" \/><\/td>\n<td style=\"width: 43.7806%;height: 14px\">4. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f1e6af317ee4fba40e391080263e08db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"138\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 56.2194%;height: 14px\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4844fe97892d599fc607627cc0def505_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#106;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#106;&#45;&#52;&#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: 43.7806%;height: 14px\">6. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-261380f82c382bddefac516440c74915_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#107;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#107;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"127\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 56.2194%;height: 14px\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d1fbdcb06ee2e225f24c9559ee04ef7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#99;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#99;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"123\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 43.7806%;height: 14px\">8. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f9c8f847e860c43a22956a208c697874_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#49;&#107;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#49;&#107;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"145\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 56.2194%;height: 14px\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5eda1656c8cbaa9e4fe541efbd95e0e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#51;&#45;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#51;&#43;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"125\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 43.7806%;height: 14px\">10. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b38b4e47d7dd4eae2bc57061352c02fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#49;&#45;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#49;&#43;&#98;&#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: 56.2194%;height: 14px\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3fa1b9f51deb2140ab27e493e07532d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#45;&#54;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#43;&#54;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 43.7806%;height: 14px\">12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c2a7cdf5c5520b0e90ce7f8bec459a55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#45;&#51;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#43;&#51;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 56.2194%;height: 14px\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-69f807f8788e1530dc05e268c19b26c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#119;&#43;&#49;&#48;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#119;&#45;&#49;&#48;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"172\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 43.7806%;height: 14px\">14. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-34996c96803a99de2d00881b3f8f5bda_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#99;&#45;&#50;&#100;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#99;&#43;&#50;&#100;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"141\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 56.2194%;height: 14px\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8fa438492b704e16d5e83508d7468d9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#53;&#125;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#53;&#125;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"153\" style=\"vertical-align: -17px;\" \/><\/td>\n<td style=\"width: 43.7806%;height: 14px\">16. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f23ff7030281f3c8ae920be585427819_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"171\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 56.2194%;height: 14px\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-62514a1785d4623997f1710dfd872ff6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#121;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#121;&#43;&#57;&#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: 43.7806%;height: 14px\">18. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a51384f26164d268b3cd3fe8df3f35e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#98;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#98;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 56.2194%;height: 14px\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-10736cf740b321d3ce823947fdb8500d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#115;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#115;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"152\" style=\"vertical-align: -17px;\" \/><\/td>\n<td style=\"width: 43.7806%;height: 14px\">20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-671ea7cf5094d6b994bef659e8a28bd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#118;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#118;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"157\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 56.2194%\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2785723b2ffc5c172f0e0d648bfe35c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#40;&#120;&#43;&#50;&#121;&#41;&#40;&#120;&#45;&#50;&#121;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 43.7806%\">22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-60f269ccd6613a10b09349e5b1263b03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#109;&#40;&#120;&#43;&#51;&#121;&#41;&#40;&#120;&#45;&#51;&#121;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"151\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 56.2194%\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bf9147541d3f0c57c61008e4f08374fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#114;&#40;&#120;&#94;&#50;&#32;&#43;&#32;&#54;&#121;&#94;&#50;&#41;&#40;&#120;&#94;&#50;&#32;&#45;&#32;&#54;&#121;&#94;&#50;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"175\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 43.7806%\">24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e16c25a60e324f8683ee5487012146eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#40;&#120;&#94;&#50;&#43;&#55;&#121;&#94;&#50;&#41;&#40;&#120;&#94;&#50;&#45;&#55;&#121;&#94;&#50;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"166\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 56.2194%\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-43a103a0d89df1f6e651fa39ebfc8de0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#53;&#120;&#94;&#51;&#32;&#43;&#32;&#121;&#94;&#51;&#41;&#40;&#53;&#120;&#94;&#51;&#32;&#45;&#32;&#121;&#94;&#51;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"156\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 43.7806%\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0c6b4ddced705b1d9ee177e2db3977e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#52;&#109;&#94;&#50;&#43;&#110;&#94;&#50;&#41;&#40;&#50;&#109;&#43;&#110;&#41;&#40;&#50;&#109;&#45;&#110;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"225\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 56.2194%\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-85ba0c7b7d27b1e4a86d2e7edd87e38b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#120;&#43;&#50;&#41;&#40;&#54;&#45;&#120;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 43.7806%\">28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fcedb83069e2c9e72c2c9b087b54dae9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#52;&#121;&#43;&#57;&#41;&#40;&#50;&#121;&#45;&#57;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"123\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 56.2194%\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-29bdacebd4409a964e3620225f7b4f75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#49;&#40;&#53;&#97;&#43;&#52;&#98;&#41;&#40;&#53;&#97;&#45;&#52;&#98;&#41;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" style=\"vertical-align: -5px;\" \/> OR <img loading=\"lazy\" decoding=\"async\" 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