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
= 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
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