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**

ab(x

By suitably rearranging the terms, we have;

= abx

= abx

= 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)

- 5 - 10t + 20t

By suitably rearranging the terms, we have;

= 20t

= 5(4t

**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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