{"id":7144,"date":"2014-06-10T17:26:49","date_gmt":"2014-06-10T17:26:49","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=7144"},"modified":"2014-12-02T08:25:29","modified_gmt":"2014-12-02T08:25:29","slug":"math-review-of-difference-of-squares","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2014\/06\/10\/math-review-of-difference-of-squares\/","title":{"rendered":"Math Review of Difference of Squares"},"content":{"rendered":"

Overview<\/h3>\n

The difference of squares is a common binomial pattern that can be factored as (x+b)(x-b). It can be used in situations involving estimation by making both elements a difference of squares.<\/p>\n

Perfect Squares<\/h3>\n

In order for the pattern to work, both elements must be perfect squares. The variable x2<\/sup> is a perfect square. So is 9x4<\/sup>, as it can be factored as (3x2<\/sup>)2<\/sup>. Similarly, the numbers 36(62<\/sup>) and 81(92<\/sup>) are perfect squares. The monomial 100x2<\/sup> can be factored as 10x(10x).<\/p>\n

Difference of Squares<\/h3>\n

Suppose the expression were 25x2<\/sup> \u2013 144. Both 25x2<\/sup> and 144 are perfect squares. The monomial 25x2<\/sup> can be factored as 5x\u22195x and 144 can be factored as 12\u221912. The entire expression can be factored as (5x +12)(5x -12). The middle terms 5x\u221912 and 5x\u2219-12 cancel each other out.<\/p>\n

Figure 1: The pattern for the difference of squares shows that the middle terms cancel each other.<\/p>\n

\"monohybridcross\"<\/a><\/p>\n

Using Estimation<\/h3>\n

A math problem such as 27\u221933 can be estimated as the difference of squares. The mean of 27 and 33 is 30, so 27 times 33 can be expressed as (30 – 3)(30 + 3) or 302<\/sup> \u2013 32<\/sup> or 900 – 9 which is 891. In order to check, 27\u221933 is 891. \u00a0Similarly, 56\u221944 can be expressed as (50 + 6)(50 – 6) or 2500 \u2013 36 = 2464, and 56\u221944 is 2464.<\/p>\n

Figure 2: An example of estimation using the difference of squares.<\/p>\n

\"monohybridcross\"<\/a><\/p>\n

Geometric Representation<\/h3>\n

Suppose one square has the area a2<\/sup> and one corner with the area measuring b2<\/sup> is taken out of it. The resulting figure, a2<\/sup>-b2<\/sup>, can be divided into 2 rectangles. One rectangle has the measurement of a(a-b). The other rectangle has the measurement of b(a-b). Adding the two rectangles together gives the measurement of (a+b)(a-b) for the same figure. The area of the figure is (a +b)(a-b), so a2<\/sup>-b2<\/sup> = (a+b)(a-b).<\/p>\n

Figure 3: Geometric representation of the difference of squares.<\/p>\n

\"monohybridcross\"<\/a><\/p>\n

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SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Edmonton, AB, Canada: visit Tutoring in Edmonton, AB, Canada<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview The difference of squares is a common binomial pattern that can be factored as (x+b)(x-b). It can be used in situations involving estimation by making both elements a difference of squares. Perfect Squares In order for the pattern to work, both elements must be perfect squares. The variable x2 is a perfect square. So […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2,10],"tags":[2725,604,1312],"class_list":["post-7144","post","type-post","status-publish","format-standard","hentry","category-algebra","category-geometry","tag-difference-of-squares","tag-estimation","tag-perfect-squares"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/7144","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=7144"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/7144\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=7144"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=7144"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=7144"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}