{"id":8861,"date":"2016-03-15T00:47:47","date_gmt":"2016-03-15T00:47:47","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=8861"},"modified":"2016-03-15T00:47:47","modified_gmt":"2016-03-15T00:47:47","slug":"math-review-of-multiplying-monomials-and-binomials-2","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-multiplying-monomials-and-binomials-2\/","title":{"rendered":"Math Review of Multiplying Monomials and Binomials"},"content":{"rendered":"

Overview<\/h3>\n

Multiplying a binomial by a monomial follows certain rules, using the distributive and associative properties.\u00a0 Multiplying a binomial by another binomial follows similar rules, and leads to the FOIL shortcut.<\/p>\n

Multiplying Monomials<\/h3>\n

Remember that monomials can be multiplied by using the properties of rational numbers and the properties of exponents.\u00a0 For example, the monomials 3x and 4x can be multiplied by using the associative and commutative properties of multiplication such that (3\u00b74) (x\u00b7x), so that 3\u00b74 equals 12, x\u00b7x equals x2<\/sup>, or 12x2<\/sup>.<\/p>\n

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

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

Multiplying a monomial by a binomial is similar, as it uses the rules for multiplying monomials, along with the distributive property.\u00a0 For example, the binomial 2x +4 can be multiplied by the monomial 4x so that (2x) (4x) equals 8x2<\/sup> and 4\u00b74x equals 16x, using the distributive property.\u00a0 Therefore, (2x +4) (4x) equals 8x2<\/sup> + 16x.\u00a0 Also, 5x (8y4<\/sup>-4x2<\/sup>-9y-11) equals 40xy4<\/sup>-20x3<\/sup>-45xy -55x.<\/p>\n

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

Multiplying Two Binomials<\/h3>\n

Multiplying a binomial by a binomial is also similar, as it uses the distributive property twice.\u00a0 For example, (x +3) (x+4) can be expanded using the distributive property once to x(x +4) +3(x +4) and again to x2<\/sup> + 4x +3x +12, or x2<\/sup> +7x +12.\u00a0 Also, (x +3) (x-5) can be expanded to x(x-5) + 3(x-5) to x2<\/sup> -5x + 3x -15, or x2<\/sup> -2x-15.<\/p>\n

Using FOIL<\/h3>\n

There is a shortcut to multiplying two binomials, so it is not necessary to remember to use the distributive property twice.\u00a0 The process is to multiply the first terms of each binomial, the outside terms of each binomial, the inside terms of each binomial, and the last terms of each binomial, or FOIL.\u00a0 Then collect the like terms by adding the outside terms.\u00a0 It gives the same result as using the distributive property twice.\u00a0 For example, (2x2<\/sup> -3) (x-2) can be multiplied by using the distributive property twice as 2x2<\/sup> (x-2) -3(x-2) or 2x3<\/sup>-4x2 –<\/sup>3x +6.\u00a0 It can also be multiplied by using FOIL, so that the first terms (2x2<\/sup>)(x) or 2x3<\/sup>, the outside terms (2x2<\/sup>)(-2) or -4x2<\/sup>, the inside terms (-3)(x) or -3x, and the last terms, (-3)(-2) or 6.<\/p>\n

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

Overview Multiplying a binomial by a monomial follows certain rules, using the distributive and associative properties.\u00a0 Multiplying a binomial by another binomial follows similar rules, and leads to the FOIL shortcut. Multiplying Monomials Remember that monomials can be multiplied by using the properties of rational numbers and the properties of exponents.\u00a0 For example, the monomials […]<\/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":[671,3893,3894],"class_list":["post-8861","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-foil","tag-multiplying-binomials","tag-multiplying-monomials"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/8861","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=8861"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/8861\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=8861"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=8861"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=8861"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}