Factorize by Regrouping The Terms to find factors of an algebraic expression. Rewrite the given expression to form different groups and take out the common factor. Finding factors is easy with the regrouping process. Follow all the problems given below and get complete knowledge on **Factorization** by Regrouping. Find the simplest method to find factors i.e. regrouping method.

## Procedure to find Factors by Regrouping

Follow the below process and solve any difficult expression factors in minutes. They are as such

Step 1: Note down the given expression. From the given algebraic expression form the groups of the given expression in such a way that a common factor can be taken out from every group.

Step 2: Factorize each group.

Step 3: At last, take out the common factor of the groups formed.

### Solved Examples on Factorization of Algebraic Expressions

1. Factoring the following expressions

(i) mn (a^{2} + b^{2}) – ab (m^{2} + n^{2})

Solution:

Given expression is mn (a^{2} + b^{2}) – ab (m^{2} + n^{2})

Rearrange the terms

mna^{2} – abm^{2} + mnb^{2} – abn^{2}

Group the first two terms and last two terms.

The first two terms are mna^{2} – abm^{2} and the second two terms are mnb^{2} – abn^{2}

Take ma^{ }common from the first two terms.

ma (na – bm)

Take -nb common from the second two terms.

-nb (na – bm)

ma (na – bm) -nb (na – bm)

Then, take (na – bm) common from the above expression.

(na – bm) (ma – nb)

The final answer is (na – bm) (ma – nb).

(ii) 2am – 4an – 3bm + 6nb

Solution:

Given expression is 2am – 4an – 3bm + 6nb

Rearrange the terms

2am – 3bm – 4an + 6nb

Group the first two terms and last two terms.

The first two terms are 2am – 3bm and the second two terms are – 4an + 6nb

Take m^{ }common from the first two terms.

m (2a – 3b)

Take -2n common from the second two terms.

-2n (2a – 3b)

m (2a – 3b) -2n (2a – 3b)

Then, take (2a – 3b) common from the above expression.

(2a – 3b) (m – 2n)

The final answer is (2a – 3b) (m – 2n).

(iii) – 6 – 12t + 18t^{2}

Solution:

Given expression is – 6 – 12t + 18t^{2}

Rearrange the terms

18t^{2 }– 12t – 6

Then, take 6 as common from the above expression.

6 (3t^{2} – 2t – 1)

The final answer is 6 (3t^{2} – 2t – 1).

2. Factorize the expression

(i) mn – m – n + 1

Solution:

Given expression is mn – m – n + 1

Rearrange the terms

mn – n – m + 1

Group the first two terms and last two terms.

The first two terms are mn – n and the second two terms are – m + 1

Take n^{ }common from the first two terms.

n (m – 1)

Take -1 common from the second two terms.

-1(m – 1)

n (m – 1) – 1(m – 1)

Then, take (m – 1) common from the above expression.

(m – 1) (n – 1)

The final answer is (m – 1) (n – 1).

(ii) pm + pn – qm – qn

Solution:

Given expression is pm + pn – qm – qn

Rearrange the terms

pm – qm + pn – qn

Group the first two terms and last two terms.

The first two terms are pm – qm and the second two terms are pn – qn

Take m^{ }common from the first two terms.

m (p – q)

Take n common from the second two terms.

n (p – q)

m (p – q) + n (p – q)

Then, take (p – q) common from the above expression.

(p – q) (m + n)

The final answer is (p – q) (m + n).