# Factorization when Binomial is Common | What is a Common Binomial?

Students can find the factors for an algebraic expression when one of its factors is binomial. Find given algebraic expression Factorization when Binomial is Common Factor. All related problems are included in this article along with a clear explanation. Therefore, students can practice every problem available in this article and improve their knowledge. The process of solving the factorization problem is very simple if you follow the procedure we explained below. Go through the complete article and learn different methods to solve factorization problems.

## Factorization of Algebraic Expressions when Binomial is Common

Follow the simple and easy guidelines on Factorization of Algebraic Expressions When Binomial is Common. They are as follows

Step 1: In the first step, find the common binomial factor.
Step 2: Note down the given expression as the product of this binomial and the quotient obtained on dividing the given expression by this binomial.

### Solved Examples on Factorization When Binomial is a Common

1. Factorize the algebraic expressions.

(i) 7b(3x – 4y) + 3a(3x – 4y)

Solution:
Given expression is 7b(3x – 4y) + 3a(3x – 4y)
In the given expression, the binomial factor is (3x – 4y) as it is common in both terms.
Take the (3x – 4y) common and multiply it with the remained terms.
(3x – 4y) (7b + 3a)

The final answer is (3x – 4y) (7b + 3a)

(ii) 12(9a + 6b)² – 4(9a + 6b)

Solution:
Given expression is 12(9a + 6b)² – 4(9a + 6b)
12 (9a + 6b) (9a + 6b) -4(9a + 6b)
In the given expression, the binomial factor is (9a + 6b) as it is common in both terms.
Take the (9a + 6b) common and multiply it with the remained terms.
(9a + 6b)(12(9a + 6b) – 4)
(9a + 6b)(108a + 72b – 48)
The final answer is (9a + 6b)(108a + 72b – 48)

2. Factorize the expression 10r(m – 2n) – 8m + 16n

Solution:
Given expression is 10r(m – 2n) – 8m + 16n
Lets take -8m  + 16n from the above equation.
Take -8 common from -8m + 16n
-8(m – 2n)
Place -8(m – 2n) in 10r(2m – 4n) – 8m + 16n equation.
10r(m – 2n) -8(m – 2n)
In the above expression, the binomial factor is (m – 2n) as it is common in both terms.
Take the (m – 2n) common and multiply it with the remained terms.
(m – 2n)(10r – 8)

The final answer is (m – 2n)(10r – 8)

3. Factorize (a – 4b)^2 – 7a + 28b

Solution:
(a – 4b)(a – 4b) – 7a + 28b
Given expression is (a – 4b)(a – 4b) – 7a + 28b
Lets take – 7a + 28b from the above equation.
Take -7 common from – 7a + 28b
-7(a – 4b)
Place -7(a – 4b) in (a – 4b)(a – 4b) – 7a + 28b equation.
(a – 4b)(a – 4b) – 7(a – 4b)
In the above expression, the binomial factor is (a – 4b) as it is common in both terms.
Take the (a – 4b) common and multiply it with the remained terms.
(a – 4b)(a – 4b – 7)

The final answer is (a – 4b)(a – 4b – 7)