Factorize by Regrouping The Terms | How to Find Factors by Regrouping?

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 (a² + b²) – ab (m² + n²)

Solution:
Given expression is mn (a² + b²) – ab (m² + n²)
Rearrange the terms
mna² – abm² + mnb² – abn²
Group the first two terms and last two terms.
The first two terms are mna² – abm²  and the second two terms are mnb² – abn²
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 + 18t²

Solution:
Given expression is – 6 – 12t + 18t²
Rearrange the terms
18t² – 12t – 6
Then, take 6 as common from the above expression.
6 (3t² – 2t – 1)

The final answer is 6 (3t² – 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).