# Factorization when Binomial is Common

In factorization when binomial is common then an algebraic expression contains a binomial as a common factor, then in order to factorize we write the expression as the products of the binomial and the quotient obtained on dividing the given expression by the binomial.

In order to factorize follow the following steps:

Step 1: Find the common binomial.

Step 2: Write the given expression as the product of this binomial and the quotient obtained on dividing the given expression by this binomial.

Solved examples of factorization when binomial is common:

1. Factorize the algebraic expressions:

(i) 5a(2x - 3y) + 2b(2x - 3y)

Solution:

5a(2x - 3y) + 2b(2x - 3y)

Here, we observe that the binomial (2x – 3y) is common to both the terms.

= (2x - 3y)(5a + 2b)

(ii) 8(4x + 5y)2 - 12(4x + 5y)

Solution:

8(4x + 5y)2 - 12(4x + 5y)

= 2 ∙ 4(4x + 5y)(4x + 5y) – 3 ∙ 4(4x + 5y)

Here, we observe that the binomial 4(4x + 5y) is common to both the terms.

= 4(4x + 5y) ∙ [2(4x + 5y) -3]

= 4(4x + 5y)(8x + 10y - 3).

2. Factorize the expression 5z(x – 2y) - 4x +8y

Solution:

5z(x – 2y) - 4x + 8y

Taking -4 as the common factor from -4x + 8y, we get

= 5z(x – 2y) – 4(x - 2y)

Here, we observe that the binomial (x – 2y) is common to both the terms.

= (x – 2y) (5z – 4)

3. Factorize (x – 3y)2 – 5x + 15y

Solution:

(x – 3y)2 – 5x + 15y

Taking – 5 common form – 5x + 15y, we get

= (x – 3y)2 – 5(x – 3y)

= (x – 3y) (x – 3y) - 5(x – 3y)

Here, we observe that the binomial (x – 3y) is common to both the terms.

= (x – 3y) [(x – 3y) – 5]

= (x – 3y) (x – 3y – 5)