{"id":6606,"date":"2014-02-19T17:41:04","date_gmt":"2014-02-19T17:41:04","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6606"},"modified":"2014-12-02T08:25:32","modified_gmt":"2014-12-02T08:25:32","slug":"addition-and-subtraction-of-polynomials","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/addition-and-subtraction-of-polynomials\/","title":{"rendered":"Addition and Subtraction of Polynomials"},"content":{"rendered":"<p><strong>Overview:<\/strong><\/p>\n<p>Polynomial expressions can be added and subtracted just like any other type of expression. However, it is important to make sure that only like terms are combined, and unlike terms are kept separate from each other.\u00a0 The resulting expression contains all the like and unlike terms of all the polynomials being considered.<\/p>\n<p><strong>What Are Like Terms?<\/strong><\/p>\n<p>Like terms contain the same variable at the same degree.\u00a0 For example, 5y and 6y are like terms because they contain the same variable y.\u00a0 Similarly, the constants 2 and 3 are like terms because they do not contain any variables.\u00a0 Also, 3x<sup>2<\/sup> and 10x<sup>2<\/sup> are also like terms.<\/p>\n<p><strong>What Are Unlike Terms?<\/strong><\/p>\n<p>Unlike terms do not contain the same variables at the same degree.\u00a0 For example, 5a and 2b cannot be added because they do not contain the same terms.\u00a0 Similarly, x<sup>4<\/sup> and x<sup>2<\/sup> cannot be combined, even though they contain the same variable, because the variable is not to the same degree.\u00a0 If a monomial, 5a, is added to another monomial, 2b, the resulting expression is a polynomial, 5a + 2b.\u00a0 Also, if a monomial, 13x<sup>2<\/sup>, is added to another monomial, 2x<sup>9<\/sup>, the resulting expression is a polynomial, 2x<sup>9<\/sup> + 13x<sup>2<\/sup>.<\/p>\n<p><strong>What About Adding Polynomials?<\/strong><\/p>\n<p>Suppose one polynomial is 5y<sup>2<\/sup>+ 10y + 25, and another one is 8y<sup>2<\/sup> + 6y &#8211; 10.\u00a0 There are two steps to adding them.\u00a0 First, it helps to group like terms together, such that (5y<sup>2<\/sup> + 8y<sup>2<\/sup>) + (10y + 6y) + (25 &#8211; 10).\u00a0 Then, add the like terms, as in (5 + 8)y<sup>2<\/sup> + (10 + 6)y + (25 &#8211; 10), using the Distributive Property.\u00a0 The end result is 13y<sup>2<\/sup> + 16y + 15.<\/p>\n<p><strong>What About Subtracting Polynomials?<\/strong><\/p>\n<p>The only difference when subtracting polynomials is to remember to use the inverse of each term that is being subtracted.\u00a0 Suppose one polynomial is 5z<sup>2<\/sup> + 9z &#8211; 30 and the one to subtract is z<sup>2<\/sup> -12z + 18.\u00a0 The like terms will be (5z<sup>2<\/sup> -z <sup>2<\/sup>) + (9z + 12z) + (-30 &#8211; 18).\u00a0 The end result will be 4z<sup>2 <\/sup>&#8211; 3z &#8211; 48.<\/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 Exeter, RI visit: <a href=\"https:\/\/schooltutoring.com\/tutoring-in-exeter-rhode-island\/\">Tutoring in Exeter, RI<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Overview: Polynomial expressions can be added and subtracted just like any other type of expression. However, it is important to make sure that only like terms are combined, and unlike terms are kept separate from each other.\u00a0 The resulting expression contains all the like and unlike terms of all the polynomials being considered. What Are [&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":[1036,1360,1910],"class_list":["post-6606","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-like-terms","tag-polynomials","tag-unlike-terms"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6606","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=6606"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6606\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6606"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6606"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6606"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}