Question

Factorise the expression $a^2-ab-ac+bc$:

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

Answer 1

The correct option is B $(a-c)(a-b)$

The given expression is
$a^2-ab-ac+bc$
Rearranging and grouping them we get
$a^2-ac-ab+bc$
= $(a^2-ac)-(ab-bc)$
= $a(a-c)-b(a-c)$ [Taking 'a' and 'b' common]
=$(a-c)(a-b)$ [Taking '(a-c)'common]