In factorization by regrouping sometimes the terms of the given 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.
Method of factoring terms:
Step 1: Arrange the terms of the given expression in groups in such a way that all the groups have a common factor.
Step 2: Factorize each group.
Step 3: Take out the factor which is common to each group.
Solved problems on factorization by regrouping the terms:
1. How to factorize the
following expressions?
(i) a^{2} + bc + ab + ac
2. Factor grouping the algebraic expressions:
(i) xy  pq + qy  px
Solution:
xy  pq + qy  px
By suitably rearranging
the terms, we have;
= (xy  px) + (qy  pq)
= x (y  p) + q (y  p)
= (y  p) (x + q).
Therefore by factoring expressions we get (y  p) (x + q).
= ax(bx + ay) + by(ay + bx)
= ax(bx + ay) + by(bx + ay)
= (bx + ay) (ax + by).
Therefore by factoring
expressions we get (bx + ay) (ax + by)
8th Grade Math Practice
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