Question

Factorise $x(x-a)-y(y-a)$

• A. $(x+y)(x+y-a)$
• B. $(x+y)(x-y-a)$
• C. $(x-y)(x+y-a)$
• D. $(x-y)(x+y)$

Answer 1

The correct option is C $(x-y)(x+y-a)$

$x(x-a)-y(y-a)$
= $x^2-ax-y^2-ay$
Re-arranging , we get
= $x^2-y^2-ax-ay$
$\text{We know}{a}^2-b^2=(a+b)(a-b)\text{taking}a\text{common}$
= $(x+y)(x-y)-a(x-y)$
Taking $(x-y)$ common
= $(x-y)(x+y-a)$