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.
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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).