# Worksheet on Factoring Binomials | Factoring Binomials Algebra Worksheets

Do you feel difficult to solve factorization problems when Binomial is a Common Factor? Don’t worry!! We have given a Worksheet on Factoring Binomials for your practice. Solve all the questions available in the Factoring Binomials Worksheets and cross-check answers to test your preparation level.

Most of the questions given in this Common Binomial Factor Worksheet impose in the exam. Therefore, students can practice and get good scores easily by practicing all the methods available in the Binomial Factorization Worksheets. Have a look at the Factorization Worksheets if you want to get a complete grip on the entire factorization concept.

## How to do Factorisation when a Binomial is a Common Factor?

1. Factorize the following binomials

(i) 3x + 21
(ii) 7a – 14
(iii) b3 + 3b
(iv) 20a + 5a2
(v) – 16m + 20m3
(vi) 5a2b + 15ab2
(vii) 9m2 + 5m
(viii) 19x – 57y
(ix) 25x2y2z3 – 15xy3z

Solution:

(i) The given expression is 3x + 21
Here, the first term is 3x and the second term is 21
By comparing the above two terms, we can observe the greatest common factor and that is 3
Now, factor out the greatest common factor from the expression
That is, 3 [x + 7]
3 [x + 7]

Therefore, the resultant value for the expression 3x + 21 is 3 [x + 7]

(ii) The given expression is 7a – 14
Here, the first term is 7a and the second term is 14
By comparing the above two terms, we can observe the greatest common factor and that is 7
Now, factor out the greatest common factor from the expression
That is, 7 [a – 2]
7 [a – 2]

Therefore, the resultant value for the expression 7a – 14 is 7 [a – 2]

(iii) The given expression is b3 + 3b
Here, the first term is b3 and the second term is 3b
By comparing the above two terms, we can observe the greatest common factor and that is b
Now, factor out the greatest common factor from the expression
That is, b [b² + 3]
b [b² + 3]

Therefore, the resultant value for the expression b3 + 3b is b [b² + 3]

(iv) The given expression is 20a + 5a2
Here, the first term is 20a and the second term is 5a2
By comparing the above two terms, we can observe the greatest common factor and that is 5a
Now, factor out the greatest common factor from the expression
That is, 5a [4 + a]
5a [4 + a]

Therefore, the resultant value for the expression 20a + 5a2 is 5a [4 + a]

(v) The given expression is – 16m + 20m3
Here, the first term is – 16m, and the second term is 20m3
By comparing the above two terms, we can observe the greatest common factor and that is 4m
Now, factor out the greatest common factor from the expression
That is, 4m [-4 + 5m²]
4m [-4 + 5m²]

Therefore, the resultant value for the expression – 16m + 20m3 is 4m [-4 + 5m²]

(vi) The given expression is 5a2b + 15ab2
Here, the first term is 5a2b and the second term is 15ab2
By comparing the above two terms, we can observe the greatest common factor and that is 5ab
Now, factor out the greatest common factor from the expression
That is, 5ab [a + 3b]
5ab [a + 3b]

Therefore, the resultant value for the expression 5a2b + 15ab2 is 5ab [a + 3b]

(vii) The given expression is 9m2 + 5m
Here, the first term is 9m2 and the second term is 5m
By comparing the above two terms, we can observe the greatest common factor and that is m
Now, factor out the greatest common factor from the expression
That is, m [9m + 5]
m [9m + 5]

Therefore, the resultant value for the expression 9m2 + 5m is m [9m + 5]

(viii) The given expression is 19x – 57y
Here, the first term is 19x and the second term is – 57y
By comparing the above two terms, we can observe the greatest common factor and that is 19
Now, factor out the greatest common factor from the expression
That is, 19 [x – 3y]
19 [x – 3y]

Therefore, the resultant value for the expression 19x – 57y is 19 [x – 3y]

(ix) The given expression is 25x2y2z3 – 15xy3z
Here, the first term is 25x2y2z3 and the second term is – 15xy3z
By comparing the above two terms, we can observe the greatest common factor and that is 5xy2z
Now, factor out the greatest common factor from the expression
That is, 5xy2z [5xz2 – 3y]
5xy2z [5xz2 – 3y]

Therefore, the resultant value for the expression 25x2y2z3 – 15xy3z is 5xy2z [5xz2 – 3y]

2. Factor each of the following algebraic expression

(i) 13x + 39
(ii) 19a – 57b
(iii) 21ab + 49abc
(iv) – 16x + 20x3
(v) 12a2b – 42abc
(vi) 27m3n3 + 36m4n2

Solution:

(i) The given expression is 13x + 39
Here, the first term is 13x and the second term is 39
By comparing the above two terms, we can observe the greatest common factor and that is 13
Now, factor out the greatest common factor from the expression
That is, 13 [x + 3]
13 [x + 3]

Therefore, the resultant value for the expression 13x + 39 is 13 [x + 3]

(ii) The given expression is 19a – 57b
Here, the first term is 19a and the second term is – 57b
By comparing the above two terms, we can observe the greatest common factor and that is 19
Now, factor out the greatest common factor from the expression
That is, 19 [a – 3b]
19 [a – 3b]

Therefore, the resultant value for the expression 19a – 57b is 19 [a – 3b]

(iii) The given expression is 21ab + 49abc
Here, the first term is 21ab and the second term is 49abc
By comparing the above two terms, we can observe the greatest common factor and that is 7ab
Now, factor out the greatest common factor from the expression
That is, 7ab [3 + 7c]
7ab [3 + 7c]

Therefore, the resultant value for the expression 21ab + 49abc is 7ab [3 + 7c]

(iv) The given expression is – 16x + 20x3
Here, the first term is – 16x and the second term is 20x3
By comparing the above two terms, we can observe the greatest common factor and that is 4x
Now, factor out the greatest common factor from the expression
That is, 4x [-4 + 5x²]
4x [-4 + 5x²]

Therefore, the resultant value for the expression – 16x + 20x3 is 4x [-4 + 5x²]

(v) The given expression is 12a2b – 42abc
Here, the first term is 12a2b and the second term is – 42abc
By comparing the above two terms, we can observe the greatest common factor and that is 6ab
Now, factor out the greatest common factor from the expression
That is, 6ab [2a – 7bc]
6ab [2a – 7bc]

Therefore, the resultant value for the expression 12a2b – 42abc is 6ab [2a – 7bc]

(vi) The given expression is 27m3n3 + 36m4n2
Here, the first term is 27m3n3 and the second term is 36m4n2
By comparing the above two terms, we can observe the greatest common factor and that is 9m3n2
Now, factor out the greatest common factor from the expression
That is, 9m3n2 [3n + 4m]
9m3n2 [3n + 4m]

Therefore, the resultant value for the expression 27m3n3 + 36m4n2 is 9m3n2 [3n + 4m]