{"id":34955,"date":"2023-10-21T13:23:54","date_gmt":"2023-10-21T07:53:54","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=34955"},"modified":"2023-11-10T11:50:45","modified_gmt":"2023-11-10T06:20:45","slug":"factorize-by-regrouping-the-terms","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/factorize-by-regrouping-the-terms\/","title":{"rendered":"Factorize by Regrouping The Terms | How to Find Factors by Regrouping?"},"content":{"rendered":"

Factorize by Regrouping The Terms to find factors of an algebraic expression. Rewrite the given expression to form different groups and take out the common factor. Finding factors is easy with the regrouping process. Follow all the problems given below and get complete knowledge on Factorization<\/strong><\/a> by Regrouping. Find the simplest method to find factors i.e. regrouping method.<\/p>\n

Procedure to find Factors by Regrouping<\/h2>\n

Follow the below process and solve any difficult expression factors in minutes. They are as such<\/p>\n

Step 1: Note down the given expression. From the given algebraic expression form the groups of the given expression in such a way that a common factor can be taken out from every group.
\nStep 2: Factorize each group.
\nStep 3: At last, take out the common factor of the groups formed.<\/p>\n

Solved Examples on Factorization of Algebraic Expressions<\/h3>\n

1. Factoring the following expressions<\/p>\n

(i) mn (a2<\/sup> + b2<\/sup>) – ab (m2<\/sup> + n2<\/sup>)<\/p>\n

Solution:
\nGiven expression is mn (a2<\/sup> + b2<\/sup>) – ab (m2<\/sup> + n2<\/sup>)
\nRearrange the terms
\nmna2<\/sup> – abm2<\/sup> + mnb2<\/sup> – abn2<\/sup>
\nGroup the first two terms and last two terms.
\nThe first two terms are mna2<\/sup> – abm2<\/sup> \u00a0and the second two terms are mnb2<\/sup> – abn2<\/sup>
\nTake ma\u00a0<\/sup>common from the first two terms.
\nma (na – bm)
\nTake -nb common from the second two terms.
\n-nb (na – bm)
\nma (na – bm) -nb (na – bm)
\nThen, take (na – bm) common from the above expression.
\n(na – bm) (ma – nb)<\/p>\n

The final answer is (na – bm) (ma – nb).<\/p>\n

(ii) 2am \u2013 4an – 3bm + 6nb<\/p>\n

Solution:
\nGiven expression is 2am \u2013 4an – 3bm + 6nb
\nRearrange the terms
\n2am – 3bm \u2013 4an + 6nb
\nGroup the first two terms and last two terms.
\nThe first two terms are 2am – 3bm and the second two terms are \u2013 4an + 6nb
\nTake m\u00a0<\/sup>common from the first two terms.
\nm (2a – 3b)
\nTake -2n common from the second two terms.
\n-2n (2a – 3b)
\nm (2a – 3b) -2n (2a – 3b)
\nThen, take (2a – 3b) common from the above expression.
\n(2a – 3b) (m – 2n)<\/p>\n

The final answer is (2a – 3b) (m – 2n).<\/p>\n

(iii) – 6 – 12t + 18t2<\/sup><\/p>\n

Solution:
\nGiven expression is – 6 – 12t + 18t2<\/sup>
\nRearrange the terms
\n18t2 <\/sup>– 12t – 6
\nThen, take 6 as common from the above expression.
\n6 (3t2<\/sup> – 2t – 1)<\/p>\n

The final answer is 6 (3t2<\/sup> – 2t – 1).<\/p>\n

2. Factorize the expression<\/p>\n

(i) mn \u2013 m \u2013 n + 1<\/p>\n

Solution:
\nGiven expression is mn \u2013 m \u2013 n + 1
\nRearrange the terms
\nmn \u2013 n \u2013 m + 1
\nGroup the first two terms and last two terms.
\nThe first two terms are mn \u2013 n and the second two terms are \u2013 m + 1
\nTake n\u00a0<\/sup>common from the first two terms.
\nn (m – 1)
\nTake -1 common from the second two terms.
\n-1(m – 1)
\nn (m – 1) – 1(m – 1)
\nThen, take (m – 1) common from the above expression.
\n(m – 1) (n – 1)<\/p>\n

The final answer is (m – 1) (n – 1).<\/p>\n

(ii) pm + pn – qm \u2013 qn<\/p>\n

Solution:
\nGiven expression is pm + pn – qm \u2013 qn
\nRearrange the terms
\npm – qm + pn \u2013 qn
\nGroup the first two terms and last two terms.
\nThe first two terms are pm – qm and the second two terms are pn \u2013 qn
\nTake m\u00a0<\/sup>common from the first two terms.
\nm (p – q)
\nTake n common from the second two terms.
\nn (p – q)
\nm (p – q) + n (p – q)
\nThen, take (p – q) common from the above expression.
\n(p – q) (m + n)<\/p>\n

The final answer is (p – q) (m + n).<\/p>\n","protected":false},"excerpt":{"rendered":"

Factorize by Regrouping The Terms to find factors of an algebraic expression. Rewrite the given expression to form different groups and take out the common factor. Finding factors is easy with the regrouping process. Follow all the problems given below and get complete knowledge on Factorization by Regrouping. Find the simplest method to find factors … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/34955"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=34955"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/34955\/revisions"}],"predecessor-version":[{"id":92674,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/34955\/revisions\/92674"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=34955"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=34955"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=34955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}