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?**

The expression is a

By suitably rearranging the terms, we have;

= a

= a(a + b) + c(a + b)

= (a + b) (a + c).

The expression is ax

By suitably rearranging the terms, we have;

= ax

= a(x

= (x

**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).

ab(x

By suitably rearranging the terms, we have;

= abx

= (abx

= 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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