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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