{"id":8867,"date":"2016-03-19T18:26:39","date_gmt":"2016-03-19T18:26:39","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=8867"},"modified":"2016-03-19T18:26:39","modified_gmt":"2016-03-19T18:26:39","slug":"math-review-of-special-products-of-binomials","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2016\/03\/19\/math-review-of-special-products-of-binomials\/","title":{"rendered":"Math Review of Special Products of Binomials"},"content":{"rendered":"

Overview<\/h3>\n

The FOIL Method is a shortcut to multiplying binomials, rather than using the distributive property twice.\u00a0 Some special products of binomials suggest other patterns, such as the product of the sum and difference of two expressions, the product of squaring the sum of an expression, and the product of squaring the difference of an expression.<\/p>\n

Review of FOIL<\/h3>\n

FOIL is an acronym for the order of multiplying terms in a product of two binomials.\u00a0 Suppose the binomials were (x +2) (x +3).\u00a0 The first step is to multiply the first terms, x\u00b7x or x2<\/sup>.\u00a0 Next, the outside terms, 3x, and then the inside terms, 2x.\u00a0 Finally, the last terms, 2\u00b73, or 6.\u00a0 Combining like terms, the product of (x + 2) (x +3) equals x2<\/sup> +5x +6.<\/p>\n

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

Sum and Difference<\/h3>\n

The product of the sum and difference of two binomials can be expressed in algebraic terms as (a +b) (a-b).\u00a0 Using FOIL, the first step is a2<\/sup>, followed by the outside step \u2013ba, followed by the inside step, ab, followed by the last step, b2<\/sup>.\u00a0 The outside \u2013ba and the inside ab cancel each other out, so combining like terms leaves (a +b) (a-b) equaling a2<\/sup> +b2<\/sup>.\u00a0 For example, (x +4) (x-4) equals x2<\/sup> -4x +4x +16 or x2<\/sup> \u2013 16.<\/p>\n

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

Squaring the Sum<\/h3>\n

Suppose each binomial is the same expression, such as (x +y) (x +y).\u00a0 Using FOIL, the first step is x2<\/sup>, followed by the outside step xy, followed by the inside step yx , followed by the last , y2<\/sup>.\u00a0 Combining like terms, x2<\/sup> +2xy +y2<\/sup> is the result.\u00a0 For example, (x +5) (x +5) equals x2<\/sup> +5x +5x +25, or x2<\/sup> +10x +25.\u00a0 Both x and 5 are squared, and the product of 5x is doubled for the middle term, rather than cancelling each other out, as in the product of the sum and difference.<\/p>\n

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

Squaring the Difference<\/h3>\n

Suppose that each binomial is a difference rather than a sum, so that the product is (x-y) (x-y).\u00a0 In that case, the first term, x2<\/sup>, is the same.\u00a0 The last term, y2<\/sup>, is also the same, because \u2013y \u00b7-y is y2<\/sup>.\u00a0 The product of two negative numbers is a positive number.\u00a0 The outside term is \u2013xy and the inside term is \u2013yx, which add to form -2xy.\u00a0 Only the sign of the middle combination has changed.\u00a0 For example, (x-6) (x-6) is x2<\/sup> -12x +36.<\/p>\n

Interested in math tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n

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 Grass Valley, CA: visit:\u00a0 Tutoring in Grass Valley, CA<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview The FOIL Method is a shortcut to multiplying binomials, rather than using the distributive property twice.\u00a0 Some special products of binomials suggest other patterns, such as the product of the sum and difference of two expressions, the product of squaring the sum of an expression, and the product of squaring the difference of an […]<\/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":[671,3895,2634],"class_list":["post-8867","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-foil","tag-multiplying-the-sum-and-difference-of-binomials","tag-squaring-a-binomial"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8867","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=8867"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8867\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=8867"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=8867"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=8867"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}