{"id":6855,"date":"2014-03-26T17:37:24","date_gmt":"2014-03-26T17:37:24","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6855"},"modified":"2014-12-02T08:25:31","modified_gmt":"2014-12-02T08:25:31","slug":"math-review-of-combining-like-terms","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-combining-like-terms\/","title":{"rendered":"Math Review of Combining Like Terms"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

One of the first steps in solving an equation is to combine like terms.\u00a0 Terms can be combined when they have the same variables and they have the same exponents.\u00a0 Otherwise they are unlike and cannot be combined to solve the equation.<\/p>\n

Real Numbers and Variables Are Unlike Terms<\/strong><\/p>\n

Suppose the expression is 3z + 9.\u00a0 The number 9 is a real number in this expression and doesn\u2019t have a variable.\u00a0 It cannot be combined with 3z until the value of z is defined.\u00a0 Similarly, suppose the expression is 7mn – 12.\u00a0 The number 12 is a real number without a variable and cannot be combined with 7mn.<\/p>\n

Combining the Same Variables<\/strong><\/p>\n

Suppose the expression is 3x + 2z.\u00a0 Those terms are in the simplest form possible, because they have two different variables, x and z.\u00a0 Until the values of x and z are defined, those expressions cannot be combined.\u00a0 However, if the expression were 4x + 2x, the variables are the same and can be added as 6x.<\/p>\n

Combining the Same Exponents<\/strong><\/p>\n

Suppose the expression is 5x2<\/sup> + x – 2z.\u00a0 That trinomial is also in the simplest form possible, because it also has three different terms that cannot be combined.\u00a0 Until the values of x and z are defined, those terms cannot be combined.\u00a0 In addition, the 5x2<\/sup> and x cannot be combined, because the value of x is not defined.\u00a0 Similarly, suppose the expression is 6a2<\/sup>b + 2ab3<\/sup>.\u00a0 Those terms cannot be combined, since even though 6a2<\/sup>b and 2ab3<\/sup> have the same variables, ab, the variables are not of the same degree.<\/p>\n

Using the Commutative and Associative Properties<\/strong><\/p>\n

Suppose the expression is 7x – 2y + 3 + 2x + 3x + 10y.\u00a0 It could be simplified by using the Commutative Property of Addition to arrange the like terms, such as 7x + 2x + 3x – 2y + 10y + 3.\u00a0 Then, the Associative Property of Addition can be used to group them together, as (7x +2x +3x) + (-2y + 10y) + 3.\u00a0 The 7x + 2x + 3x can be simplified as 12x and the – 2y + 10y can be simplified as 8y.\u00a0 The best expression is then 12x + 8y + 3.<\/p>\n

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Overview: One of the first steps in solving an equation is to combine like terms.\u00a0 Terms can be combined when they have the same variables and they have the same exponents.\u00a0 Otherwise they are unlike and cannot be combined to solve the equation. Real Numbers and Variables Are Unlike Terms Suppose the expression is 3z […]<\/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":[634,1036,1926],"class_list":["post-6855","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-exponents","tag-like-terms","tag-variables"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6855","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=6855"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6855\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6855"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6855"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6855"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}