Worksheet on Factoring out a Common Binomial Factor is available with a number of different problems and solutions. The Binomial Factorization Worksheet is available as per the new syllabus instructions. Learn and practice more problems on the factorization of a common binomial factor with the help of the given worksheet. We have explained every problem with the simplest method to help students clearly understand how to factor out a common binomial factor of an algebraic expression.

Also, check out all Factorization Worksheets and practice all problems for better results.

## Solved Problems on Factoring Out a Common Binomial Factor

1. Factorize by taking binomial as a common factor

(i) 3(a + 2) + 7(a + 2)

(ii) (a + 3)a + (a + 3)4.

(iii) 2(5a + 3b) + c(5a + 3b).

(iv) 3a(b – 4c) – 5d(b – 4c).

(v) x(p – q) + y (q – p).

## Solution:

(i) The given expression is 3(a + 2) + 7(a + 2).

Factor out the common terms from the above expression. That is,

(a + 2) (3 + 7)

10 (a + 2).

The final answer is 10 (a + 2).

(ii) The given expression is (a + 3)a + (a + 3)4.

Factor out the common term from the above expression. That is,

(a + 3) (a + 4).

The final answer is (a + 3) (a + 4).

(iii) The given expression is 2(5a + 3b) + c(5a + 3b).

Factor out the common term from the above expression. That is,

(5a + 3b) (2 + c).

The final answer is (5a + 3b) (2 + c).

(iv) The given expression is 3a(b – 4c) – 5d(b – 4c).

Factor out the common term from the above expression. That is,

(b – 4c) (3a – 5d).

The final answer is (b – 4c) (3a – 5d).

(v) The given expression is x(p – q) + y(q – p).

x(p – q) – y(- q + p).

x(p – q) – y(p – q).

Factor out the common terms from the above expression. That is,

(p – q) (x – y).

The final answer is (p – q) (x – y).

2. Factorize a common binomial factor from each of the following expression

(i) p(q + r) – s (q + r).

(ii) 12(ab + 1) + 3x (ab + 1).

(iii) x^2 + y^2 + 9p (x^2 + y^2).

(iv) 3(x + y) – 5(x + y)^2.

## Solution:

(i) The given expression is p (q + r) – s (q + r).

Factor out the common terms from the above expression. That is,

(q + r) (p – s).

The final answer is (q + r) (p – s).

(ii) The given expression is 12(ab + 1) + 3x (ab + 1).

Factor out the common terms from the above expression. That is,

(ab + 1) (12 + 3x).

The final answer is (ab + 1) (12 + 3x).

(iii) The given expression is x^2 + y^2 + 9p(x^2 + y^2).

Factor out the common terms from the above expression. That is,

(x^2 + y^2) (1 + 9p).

The final answer is (x^2 + y^2) (1 + 9p).

(iv) The given expression is 3(x + y) – 5(x + y)^2.

Factor out the common terms from the above expression. That is,

(x + y) (3 – 5(x + y)).

(x + y) (3 – 5x – 5y).

The final answer is (x + y) (3 – 5x – 5y).

3. Factorize common binomial factor from each of the following expressions

(i) x (3y – 7z) – z (3y – 7z).

(ii) (2x – 6) (3p – 2q) – (2x – 6) (2q – 3p).

(iii) a (a + b) + (5a + 5b).

(iv) (6ab + 3a) + (2b + 1).

(v) a (b – c)^2 – d (c – b)^3.

(vi) (a – 3) + (3xy – xya)

## Solution:

(i) The given expression is x (3y – 7z) – z (3y – 7z).

Factor out the common terms from the above expression. That is,

(3y – 7z) (x – z).

The final answer is (3y – 7z) (x – z).

(ii) The given expression is (2x – 6) (3p – 2q) – (2x – 6) (2q – 3p).

(2x – 6) (3p – 2q) – (2x – 6) ( – ) (3p – 2q).

(2x – 6) (3p – 2q) + (2x – 6) (3p – 2q).

Factor out the common terms from the above expression. That is,

2(2x – 6) (3p – 2q).

The final answer is 2(2x – 6) (3p – 2q).

(iii) The given expression is a(a + b) + (5a + 5b).

a(a + b) + 5(a + b).

Factor out the common terms from the above expression. That is,

(a + b) (a + 5).

The final answer is (a + b) (a + 5).

(iv) The given expression is (6ab + 3a) + (2b + 1).

3a(2b + 1) + (2b + 1).

Factor out the common terms from the above expression. That is,

(2b + 1) (3a + 1).

The final answer is (2b + 1) (3a + 1).

(v) The given expression is a(b – c)^2 – d(c – b)^3.

a(b – c)^2 + d(b – c)^3.

Factor out the common terms from the above expression. That is,

(b – c)^2 [a + d(b – c)].

The final answer is (b – c)^2 [a + d(b – c)].

(vi) The given expression is (a – 3) + (3xy – xya).

(a – 3) + xy( 3 – a).

(a – 3) – xy (a – 3).

Factor out the common terms from the above expression. That is,

(a – 3) (1 – xy).

The final answer is (a – 3) (1 – xy).