Factoring Terms by Regrouping

Factoring terms by regrouping (two or more) means that you need to rearrange the terms with common factors before factoring. In case of regrouping the terms of the given algebraic expression need to be arranged in suitable groups in such a way that all the groups have a common factor. After this arrangement factorization becomes easy.

Solved examples on factoring terms by regrouping:

1. Factorize the expression:

(i) a2x + abx + ac + aby + b2y + bc

Solution:

a2x + abx + ac + aby + b2y + bc

By suitably rearranging the terms, we have;

= a2x + abx + aby + b2y + ac + bc

= ax(a + b) + by(a + b) + c(a + b)

= (a + b) (ax + by + c)



(ii) p3k + p2(k – m) – p(m + n) – n

Solution:

p3k + p2(k – m) – p (m + n) – n

By suitably rearranging the terms, we have;

= p3k + p2k – p2m – pm – pn – n

= (p3k + p2k) – (p2m + pm) – (pn + n)

= p2k (p + 1) - pm (p + 1) – n (p + 1)

= (p + 1) (p2k – pm – n)


2. How to factorize by grouping the following expressions?

(i) ax – bx + by + cy – cx – ay

Solution: 

ax – bx + by + cy – cx – ay

By suitably rearranging the terms, we have; 

= ax - bx – cx – ay + by + cy

= x(a – b – c) - y(a – b – c) 

(a – b – c) (x - y)


(ii) x3 - 2x2 + ax + x - 2a – 2

Solution:

x3 - 2x2 + ax + x - 2a – 2

By suitably rearranging the terms, we have;

= x3 - 2x2 + ax - 2a + x - 2

= (x3 - 2x2) + (ax - 2a) + (x - 2)

= x2(x - 2) + a(x - 2) + 1(x - 2)

= (x - 2) (x2 + a + 1)








8th Grade Math Practice

From Factoring Terms by Regrouping to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. 2nd grade math Worksheets | Free Math Worksheets | By Grade and Topic

    Dec 06, 23 01:23 AM

    2nd Grade Math Worksheet
    2nd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students.

    Read More

  2. Rupees and Paise | Paise Coins | Rupee Coins | Rupee Notes

    Dec 04, 23 02:14 PM

    Different types of Indian Coins
    Money consists of rupees and paise; we require money to purchase things. 100 paise make one rupee. List of paise and rupees in the shape of coins and notes:

    Read More

  3. Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

    Dec 04, 23 01:50 PM

    Months of the Year
    There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

    Read More