{"id":8892,"date":"2016-04-03T01:45:15","date_gmt":"2016-04-03T01:45:15","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=8892"},"modified":"2016-04-03T01:45:15","modified_gmt":"2016-04-03T01:45:15","slug":"math-review-of-multiplying-polynomials","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2016\/04\/03\/math-review-of-multiplying-polynomials\/","title":{"rendered":"Math Review of Multiplying Polynomials"},"content":{"rendered":"

Overview<\/h3>\n

Multiplying two polynomials is similar to multiplying a polynomial by a monomial, or multiplying a binomial by another binomial.\u00a0 It uses the same principle of multiplying each term by every other term.<\/p>\n

Multiplying a Polynomial by a Monomial<\/h3>\n

Remember when multiplying a polynomial by a monomial to multiply each term of the binomial by using the distributive property.\u00a0 Then like terms can be combined.\u00a0 For example, 4x2<\/sup>(-2x3<\/sup> + 5x2<\/sup> + 10) means the same thing as (4x2<\/sup>) (-2x3<\/sup>) + (4x2<\/sup>) (5x2<\/sup>) + (4x2<\/sup>) (10) or -8x5<\/sup> + 20x4<\/sup> + 40x2<\/sup>.\u00a0 Notice that multiplying each term uses the rules of multiplying numerical coefficients, such as 4\u00b7-2 equals -8, 4\u00b75 equals 20, and 4\u00b710 equals 40.\u00a0 Multiplying each term also uses the rule of multiplying exponents.<\/p>\n

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Special Products of Binomials<\/h3>\n

When multiplying binomials, each term of one binomial must be also multiplied by each term of the other binomial.\u00a0 The distributive property is also used and like terms can be combined.\u00a0 For special binomials, shortcuts can speed the process.\u00a0 For example, any binomial (A + B) 2<\/sup> equals A2<\/sup> + 2AB + B2<\/sup>, and any binomial (A-B) 2<\/sup> equals A2<\/sup>– 2AB + B2<\/sup>.\u00a0 Similarly, (A + B) (A-B), also known as the sum and difference of two binomials, always equals A2<\/sup> \u2013 B2<\/sup>.<\/p>\n

Using FOIL<\/h3>\n

Any two binomials, whether they are special products or not can be multiplied by using the acronym FOIL, as a mnemonic to ensure all terms in one binomial are being multiplied by all terms in the other binomial.\u00a0 Using FOIL, the first<\/strong> terms are multiplied, the outer<\/strong> terms, the inner<\/strong> terms, and the last<\/strong> terms.\u00a0 Then like terms are combined.\u00a0 For example, when multiplying (x +5)(x +6), the first<\/strong> terms are x\u00b7x, or x2<\/sup>.\u00a0 The outer<\/strong> terms are 6\u00b7x, or 6x, and the inner<\/strong> terms are 5\u00b7x, or 5x.\u00a0 Then, 5x and 6x are like terms and can be added, as 11x.\u00a0 Finally the last<\/strong> terms, 5\u00b76, or 30 can be combined.\u00a0 The entire equation is (x +5) (x +6) equals x2<\/sup> +11x +30.<\/p>\n

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Multiplying Polynomials<\/h3>\n

Multiplying polynomials is similar to multiplying monomials and binomials, except that every term in one polynomial is multiplied by every other term in the other polynomial. Suppose the equation is (x2<\/sup> + 2x +3) (4x +5).\u00a0 Start by multiplying x2<\/sup> by 4x, or 4x3<\/sup>, then x2<\/sup> by 5 or 5x2<\/sup>.\u00a0 Next, 2x by 4x or 8x2<\/sup>.\u00a0 Next 3 by 4x gives 12x and 3 times 5 is 15.\u00a0 \u00a0That leaves 4x3<\/sup> + 5x2<\/sup> + 8x2<\/sup> + 12x + 15.\u00a0\u00a0\u00a0\u00a0 Finally, combine like terms, since 5x2<\/sup> +8x2<\/sup> equals 13x2<\/sup>, so that the equation in simplest terms is 4x3<\/sup> + 13x2<\/sup> + 12x +15.<\/p>\n

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 <\/p>\n","protected":false},"excerpt":{"rendered":"

Overview Multiplying two polynomials is similar to multiplying a polynomial by a monomial, or multiplying a binomial by another binomial.\u00a0 It uses the same principle of multiplying each term by every other term. Multiplying a Polynomial by a Monomial Remember when multiplying a polynomial by a monomial to multiply each term of the binomial by […]<\/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":[3732,3902,3903],"class_list":["post-8892","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-combining-like-terms","tag-multiplying-polynomials","tag-using-foil"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8892","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=8892"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8892\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=8892"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=8892"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=8892"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}