Question

$\text{Which of the following are the factors of}{a}^2+b-ab-a?$

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

Answer 1

The correct option is A $(a-1)and(a-b)$

Given the expression $a^2+b-ab-a.$

The above expression can be written as $a^2-ab+b-a.$

Taking $a$ as a common factor from the first two terms and $-1$ from the last two terms, we get
$a(a-b)-1(a-b).$

Here, $a-b$ is a common factor. Factoring it out, we get
$(a-b)(a-1).$

$\therefore a^2+b-ab-a=(a-b)(a-1)$

Therefore, $(a-1)$ and $(a-b)$ are factors of the given expression.