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Question

The factors of a2+b−ab−a are :


A

(a−1)(a−b)

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B

(a+b)(a−1)

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C

(a+1)(a−b)

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D

(a+1)(a+b)

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Solution

The correct option is A

(a−1)(a−b)


Consider the given expression,

a2+b−ab−a......(i)

Rearranging the terms of expression (i), we get
=(a2−ab)+(b−a).....(ii)

Taking a common from first two terms and -1 from last two terms of expression (ii), we get
=a(a−b)−1(a−b)...(iii)

Taking (a−b) common from expression (iii), we get
=(a−b)(a−1)

Therefore , the factors of a2+b−ab−a are (a−b) and (a−1).

i.e., a2+b−ab−a =(a−b)(a−1)


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