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
grouping the algebraic expressions:
(i) xy - pq + qy - px
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).
(ii) ab(x2 + y2) + xy(a2 + b2).
= 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)