# Binomial is a Common Factor | Factorisation when a Binomial is Common

All solved examples of Factorization problems when Binomial is a common factor are included in this article. Check how to find the binomial factor and practice all problems given here. Compare the terms in the given expression and factor out the greatest common factor term from the expression. Based on the greatest common factor, we will get the solution for the expression that is in terms of the product of two or more terms.

## How to Factorize taking out the Binomial Common Factor?

Go through the below step by step procedure and do Factorization when a Binomial is a Common Factor. They are along the lines

1. Note down the given expression
2. Note down the first term and second term from the expression
3. Compare the two terms and observe the greatest common factor
4. Now, factor out the greatest common factor from the expression
5. Finally, we will get the result in the form of the product of two or more terms.

### Solved Binomial Factor Examples

1. Factorize the expression (6x + 1)Â² â€“ 5(6x + 1)?

Solution:
The given expression is (6x + 1)Â² â€“ 5(6x + 1)
Here, the first term is (6x + 1)Â² and second term is â€“ 5(6x + 1)
By comparing the above two terms, we can observe the greatest common factor and that is (6x + 1)
Now, factor out the greatest common factor from the expression
That is, (6x + 1) [(6x + 1) â€“ 5]
(6x + 1)(6x â€“ 4)

Therefore, the resultant value for the expression (6x + 1)Â² â€“ 5(6x + 1) is (6x + 1)(6x â€“ 4)

2. Factorize the algebraic expression 4x(y – z) + 3(y â€“ z)?

Solution:
The given expression is 4x(y â€“ z) + 3(y â€“ z)
Here, the first term is 4x(y â€“ z) and the second term is 3(y â€“ z)
By comparing the above two terms, we can observe the greatest common factor and that is (y – z)
Now, factor out the greatest common factor from the expression
That is, (y â€“ z)(4x + 3)

Therefore, the resultant value for the expression 4x(y â€“ z) + 3(y â€“ z) is (y â€“ z)(4x + 3)

3. Factorize the expression (3x â€“ 4y) (p â€“ q) + (3x â€“ 2y) (p â€“ q)?

Solution:
The given expression is (3x â€“ 4y) (p â€“ q) + (3x â€“ 2y) (p â€“ q)
Here, the first term is (3x â€“ 4y) (p â€“ q) and the second term is (3x â€“ 2y) (p â€“ q)
By comparing the above two terms, we can observe the greatest common factor and that is (p â€“ q)
Now, factor out the greatest common factor from the expression
That is, (p â€“ q)[(3x â€“ 4y) + (3x â€“ 2y)]
= (p â€“ q)(6x â€“ 6y)

Therefore, the resultant value for the expression (3x â€“ 4y) (p â€“ q) + (3x â€“ 2y) (p â€“ q) is (p â€“ q)(6x â€“ 6y)

4. Factorize the expression 6(2x + y)Â² +8(2x + y)?

Solution:
The given expression is 6(2x + y)Â² +8(2x + y)
Here, the first term is 6(2x + y)Â² and the second term is 8(2x + y)
By comparing the above two terms, we can observe the greatest common factor and that is (2x + y)
Now, factor out the greatest common factor from the expression
That is, (2x + y)[6(2x + y) + 8]
(2x + y)(12x + 6y + 8)

Therefore, the resultant value for the expression 6(2x + y)Â² +8(2x + y) is (2x + y)(12x + 6y + 8)

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