{"id":6631,"date":"2014-02-20T17:22:54","date_gmt":"2014-02-20T17:22:54","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6631"},"modified":"2014-12-02T08:25:32","modified_gmt":"2014-12-02T08:25:32","slug":"multiplication-of-polynomials","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/multiplication-of-polynomials\/","title":{"rendered":"Multiplication of Polynomials"},"content":{"rendered":"<p><strong>Overview<\/strong><\/p>\n<p>Polynomials can be multiplied similarly to operations with monomials.\u00a0 There are two different types of properties used, the Distributive Property, and properties of multiplying exponents.\u00a0 In addition, like terms can be combined to simplify the resulting equation.<\/p>\n<p><strong>Multiplying a Monomial by a Polynomial<\/strong><\/p>\n<p>In some types of expressions, a monomial is multiplied by a polynomial.\u00a0 For example, suppose the problem is to find the area of a rectangle that measures 2x on one side and 4x + 3 on the other side.\u00a0 The product will be 2x(4x + 3).\u00a0 Using the Distributive Property, 2x(4x) + 2x(3) will be the final expression.\u00a0 The first term, 2x(4x), can be simplified to 8x<sup>2<\/sup>.\u00a0 The second term, 2x(3), can be simplified to 6x.\u00a0 The final expression is 8x<sup>2<\/sup> + 6x.<\/p>\n<p><strong>Multiplying a Polynomial by a Polynomial<\/strong><\/p>\n<p>Multiplying a polynomial by another polynomial requires an additional step.\u00a0 Suppose the problem is to find the area of a rectangle that measures 2x + 1 on one side and 3x + 3 on the other side.\u00a0 The product will be a little more complicated, (2x + 1)(3x + 3).\u00a0 It will also use the Distributive Property, as well as properties of exponents.<\/p>\n<p><strong>Use the Distributive Property Twice<\/strong><\/p>\n<p>The expression can be expanded to (2x + 1)3x + (2x + 1)3. Since there are two terms in the first polynomial and two terms in the second polynomial, the Distributive Property is actually used twice, once for the first polynomial and once for the second polynomial.\u00a0 Solving the expression results in two sets of terms (2x)(3x) + 3x + (2x)3 + 3(1), or 6x<sup>2<\/sup> + 3x + 6x + 3.<\/p>\n<p><strong>Combining Like Terms<\/strong><\/p>\n<p>The last step in the multiplication is to combine like terms at the same degree.\u00a0 There is only one quadratic term, 6x<sup>2<\/sup>, two linear terms 3x + 6x equaling 9x , and one constant, 3.\u00a0 The final expression is 6x<sup>2<\/sup> + 9x + 3.<\/p>\n<p>Interested in <a href=\"https:\/\/schooltutoring.com\/math-tutoring\/algebra-1-tutoring\/\">algebra tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n<p><span class=\"tutorOrange\">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 Provo, UT visit:<a href=\"https:\/\/schooltutoring.com\/tutoring-in-provo-utah\/\"> Tutoring in Provo, UT<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Overview Polynomials can be multiplied similarly to operations with monomials.\u00a0 There are two different types of properties used, the Distributive Property, and properties of multiplying exponents.\u00a0 In addition, like terms can be combined to simplify the resulting equation. Multiplying a Monomial by a Polynomial In some types of expressions, a monomial is multiplied by a [&hellip;]<\/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":[1147,1360],"class_list":["post-6631","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-monomials-distributive-property","tag-polynomials"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6631","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=6631"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6631\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6631"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6631"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6631"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}