Practice the worksheet on factoring out a common binomial factor from a polynomial expression which is similar to factoring using G.C.F.
We know, G.C.F of some of the terms is a binomial instead of monomial. In such cases we can factor the entire binomial from the expression. Thus, this find of binomial which is the G.C.F of more than one term in a polynomial is called the common binomial factor.
1. Factorize by taking binomial as a common factor:
(i) 3(x + 5) + 7(x + 5)
(ii) (x + 4)x + (x + 4)5
(iii) 2(5x + 3y) + z(5x + 3y)
(iv) 3r(x – 4y) – 5p(x – 4y)
(v) b(x – y) + a (y – x)
Hint: (y – x) to – (x – y)
2. Factorize a common binomial factor from each of the following
expression:
(i) x(a + b) – y(a + b)
(ii) 15(pq + 1) + 3r(pq + 1)
(iii) l^{2} + m^{2} + 9a(l^{2} + m^{2})(v) l(3m – 7n)  n(3m – 7n)
(vi) (2m – 5) (3a  2b)  (2m – 5) (2b – 3a)
(vii) x(x + y) + (5x + 5y)
(viii) (6xy + 3x) + (2y + 1)
(ix) p(q – r)^{2} – s(r  q)^{3}(x) (c – 3) + (3ab – abc)
Hint : 3ab – abc = ab(3  c) =  ab(c – 3)
Answers for the worksheet on factoring out a common binomial factor are given below to check the exact answers of the above factorization.
Answers:
1. (i) 10(x + 5)
(ii) (x + 4) (x + 5)
(iii) (5x + 3y) (2 + z)
(iv) (x – 4y) (3r  5p)
(v) (x – y) (b – a)
2. (i) (a + b) (x – y)
(ii) 3(pq +1) (5 + r )
(iii) (l^{2} + m^{2}) (1 + 9a)(iv) (l + m) (3 – 5l – 5m)
(v) (3m – 7n) (l – n)
(vi) 2(2m – 5) (3a – 2b)
(vii) (x + y) (x + 5)
(viii) (3x + 1) (2y + 1) (ix) (q – r)^{2} (p + sq – sr)(x) (1 – ab) (c – s)
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