Question

The factors of $a^2+b-ab-a$ are :

• A. $(a-1)(a-b)$
• B. $(a+b)(a-1)$
• C. $(a+1)(a-b)$
• D. $(a+1)(a+b)$

Answer 1

The correct option is A

$(a-1)(a-b)$

Consider the given expression,

$a^2+b-ab-a$......(i)

Rearranging the terms of expression (i), we get
$=(a^2-ab)+(b-a)$.....(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 $a^2+b-ab-a$ are $(a-b)$ and $(a-1)$.

i.e., $a^2+b-ab-a$ $=(a-b)(a-1)$