{"id":34960,"date":"2023-10-21T13:26:09","date_gmt":"2023-10-21T07:56:09","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=34960"},"modified":"2023-11-10T11:50:33","modified_gmt":"2023-11-10T06:20:33","slug":"factoring-terms-by-regrouping","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/factoring-terms-by-regrouping\/","title":{"rendered":"Factoring Terms by Regrouping | Factoring by Regrouping Steps, Examples"},"content":{"rendered":"

Factoring Terms by Regrouping concept and examples are given in this article. Students who are searching for the best way to solve problems of finding factors can follow this article. All the tricks and tips to learn Factorization<\/strong><\/a> problems are given in this article. All the students need to do is solve all the problems and test their knowledge. Score good marks in the exam by solving all the problems given in this article.<\/p>\n

Factoring Terms by Regrouping Solved Examples<\/h2>\n

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

(i) p2<\/sup>r + pqr + pc + pqs + q2<\/sup>s + qc<\/p>\n

Solution:
\nGiven expression is p2<\/sup>r + pqr + pc + pqs + q2<\/sup>s + qc
\nRearrange the terms
\np2<\/sup>r + pqr + pqs + q2<\/sup>s + pc + qc
\nGroup the first two terms, middle two terms, and last two terms.
\nThe first two terms are\u00a0p2<\/sup>r + pqr, middle terms are pqs + q2<\/sup>s, and the last two terms are pc + qc
\nTake pr\u00a0<\/sup>common from the first two terms.
\npr (p + q)
\nTake qs common from the second two terms.
\nqs (p + q)
\nTake c common from the last two terms.
\nc (p + q)
\npr (p + q) + qs (p + q) + c (p + q)
\nThen, take (p + q) common from the above expression.
\n(p + q) (pr + qs + c)<\/p>\n

The final answer is (p + q) (pr + qs + c).<\/p>\n

(ii) s3<\/sup>k + s2<\/sup>(k \u2013 m) \u2013 s(m + n) \u2013 n<\/p>\n

Solution:
\nGiven expression is s3<\/sup>k + s2<\/sup>(k \u2013 m) \u2013 s(m + n) \u2013 n
\nRearrange the terms
\ns3<\/sup>k + s2<\/sup>k \u2013 s2<\/sup>m \u2013 sm \u2013 sn \u2013 n
\nGroup the first two terms, middle two terms, and last two terms.
\nThe first two terms are s3<\/sup>k + s2<\/sup>k, the middle terms are \u2013 s2<\/sup>m \u2013 sm, and the second two terms are \u2013 sn \u2013 n
\nTake s2<\/sup>k\u00a0<\/sup>common from the first two terms.
\ns2<\/sup>k (s + 1)
\nTake \u2013 sm common from the middle two terms.
\n\u2013 sm (s + 1)
\nTake -n common from the last two terms.
\n-n (s + 1)
\ns2<\/sup>k (s + 1) \u2013 sm (s + 1) – n (s + 1)
\nThen, take (s + 1) common from the above expression.
\n(s + 1) (s2<\/sup>k \u2013 sm – n)<\/p>\n

The final answer is (s + 1) (s2<\/sup>k \u2013 sm – n).<\/p>\n

2. How to factorize by grouping the following expressions?<\/p>\n

(i) px \u2013 qx + qy + ry \u2013 rx \u2013 py<\/p>\n

Solution:
\nGiven expression is px \u2013 qx + qy + ry \u2013 rx \u2013 py
\nRearrange the terms
\npx \u2013 qx \u2013 rx + qy + ry \u2013 py
\nGroup the first three terms, and last three terms.
\nThe first three terms are px \u2013 qx \u2013 rx, and the last three terms are qy + ry \u2013 py
\nTake x\u00a0<\/sup>common from the first three terms.
\nx (p – q – r)
\nTake y common from the last three terms.
\n-y (p – q – r)
\nx (p – q – r) – y (p – q – r)
\nThen, take (p – q – r) common from the above expression.
\n(p – q – r) (x – y)<\/p>\n

The final answer is (p – q – r) (x – y).<\/p>\n

(ii) a3<\/sup> – 2a2<\/sup> + ma + a – 2m \u2013 2<\/p>\n

Solution:
\nGiven expression is a3<\/sup> – 2a2<\/sup> + ma + a – 2m \u2013 2
\nRearrange the terms
\na3<\/sup> – 2a2<\/sup> + ma – 2m+ a \u2013 2
\nGroup the first two terms, middle two terms, and last two terms.
\nThe first two terms are a3<\/sup> – 2a2<\/sup>, the middle terms are ma – 2m, and the last two terms are a \u2013 2
\nTake a2<\/sup>\u00a0<\/sup>common from the first two terms.
\na2<\/sup> (a – 2)
\nTake m common from the middle two terms.
\nm (a – 2)
\nTake 1 common from the last two terms.
\n1 (a – 2)
\na2<\/sup> (a – 2) + m (a – 2) + 1 (a – 2)
\nThen, take (a – 2) common from the above expression.
\n(a – 2) (a2<\/sup> + m + 1)<\/p>\n

The final answer is (a – 2) (a2 + m + 1).<\/p>\n","protected":false},"excerpt":{"rendered":"

Factoring Terms by Regrouping concept and examples are given in this article. Students who are searching for the best way to solve problems of finding factors can follow this article. All the tricks and tips to learn Factorization problems are given in this article. All the students need to do is solve all the problems … 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\/34960"}],"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=34960"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/34960\/revisions"}],"predecessor-version":[{"id":92673,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/34960\/revisions\/92673"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=34960"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=34960"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=34960"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}