In factorize by regrouping the terms sometimes it is observed that all the terms of the expression do not have any common factor, neither a monomial nor a binomial.
Follow the steps to factorize by regrouping the terms:
Step 1: From the algebraic expression arrange the groups of the given expression in such a way, that a common factor can be taken out from each group.
Step 2: Factorize each group.
Step 3: Now take out the common factor of the groups formed.
Examples to factorize algebraic expressions:
1. Factoring the following expressions
(i) ab (x^{2} + y^{2})  xy (a^{2} + b^{2})= ax(bx  ay)  by(bx  ay)
= (bx  ay) (ax  by)
(ii) 2ax – 4ay  3bx + 6y
Solution:
2ax – 4ay  3bx + 6y
By suitably rearranging the terms, we have;
= 2ax – 3bx – 4ay + 6by
= x(2a – 3b)  2y(2a – 3b)
= (2a – 3b) (x  2y)
2. Factorize the expression:
(i) ab – a – b + 1
Solution:
ab – a – b + 1
By suitably rearranging the terms, we have;
= ab – b – a + 1
= b(a  1)  1(a  1)
= (a  1) (b  1)
(ii) ax + ay  bx – by
Solution:
ax + ay  bx – by
By suitably rearranging the terms, we have;
= ax  bx + ay  by
= (ax  bx) + (ay  by)
= x(a  b) + y(a  b)
= (a  b) (x + y)
8th Grade Math Practice
From Factorize by Regrouping The Terms to HOME PAGE
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.

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.