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
From Factorization by Regrouping 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.
