{"id":6634,"date":"2014-02-21T17:37:56","date_gmt":"2014-02-21T17:37:56","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=6634"},"modified":"2014-12-02T08:25:32","modified_gmt":"2014-12-02T08:25:32","slug":"math-review-of-squaring-binomials","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2014\/02\/21\/math-review-of-squaring-binomials\/","title":{"rendered":"Math Review of Squaring Binomials"},"content":{"rendered":"

Overview<\/strong><\/p>\n

When binomials are squared, the resulting trinomial follows a pattern.\u00a0 The pattern can be derived from the general process of multiplying a binomial by another binomial, except that all the terms are the same.\u00a0 As in the general process, the Distributive Property is used, then like terms are combined.<\/p>\n

What Is A Squared Binomial?<\/strong><\/p>\n

A squared binomial is a polynomial with two terms multiplied by itself.\u00a0 For example, 2x + 5 is a binomial, multiplied by itself is (2x + 5)(2x + 5).\u00a0 Similarly (y – 2) is a binomial, multiplied by itself is (y – 2)(y – 2).\u00a0 The concept of squaring a binomial is no different than squaring any number or variable.<\/p>\n

Expanding the Expression and Combining Like Terms<\/strong><\/p>\n

The expression (2x + 5)(2x + 5) can be expanded using the Distributive Property, so that solving it results in the expression 2x(2x + 5) + 5(2x + 5) or 4x2<\/sup> + 10x + 10x + 25.\u00a0 Combining like terms results in the expression 4x2<\/sup> + 20x + 25.\u00a0 Similarly, expanding (y-2)2<\/sup> results in y(y-2) – 2(y-2) or y2<\/sup>-2y – 2y + 4.\u00a0 (Multiplying -2 by -2 results in 4.)\u00a0 Combining like terms results in the expression y2<\/sup>– 4y + 4.<\/p>\n

What Is the Pattern for Squaring a Binomial Sum?<\/strong><\/p>\n

A binomial sum is in the pattern a + b, so the square is in the form of (a + b)(a + b) algebraically.\u00a0 The general pattern for squaring a sum can be found by multiplying the terms and then combining like terms.\u00a0 Using the Distributive Property, the resulting expansion is a(a + b) + b(a + b).\u00a0 It doesn’t matter if b is another variable or a constant real number.\u00a0 The result is a2<\/sup> +ab + ba + b2<\/sup>.\u00a0 Combining like terms (because ab and ba are the same because of the Commutative Property), the resulting pattern is a2<\/sup> + 2ab + b2<\/sup>.<\/p>\n

What Is the Pattern for Squaring a Binomial Difference?<\/strong><\/p>\n

A binomial difference is in the pattern a – b, so the square is in the form of (a-b)(a-b).\u00a0 The general pattern is very similar to the pattern for squaring a binomial sum, except that it is important to watch the signs.\u00a0 The expression a(a – b) – b(a – b) results in the expansion a2<\/sup>-ab – ba + b2<\/sup>.\u00a0 Two negative numbers multiplied results in a positive number, just as it did when -2 was multiplied by -2 to result in 4.\u00a0 The resulting pattern is a2<\/sup>– 2ab + b2<\/sup>.\u00a0 Those patterns are a shortcut to factoring polynomials.<\/p>\n

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Overview When binomials are squared, the resulting trinomial follows a pattern.\u00a0 The pattern can be derived from the general process of multiplying a binomial by another binomial, except that all the terms are the same.\u00a0 As in the general process, the Distributive Property is used, then like terms are combined. What Is A Squared Binomial? […]<\/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],"tags":[193,194,1719],"class_list":["post-6634","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-binomial-difference","tag-binomial-sum","tag-squared-binomials"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6634","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=6634"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6634\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6634"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6634"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6634"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}