Question

Factorize the following algebraic expression:

$x^2-y^2+6y-9$

Answer 1

Given: $x^2-y^2+6y-9$
$=x^2-(y^2-6y+9)$
$=x^2-[y^2-2(y\left)\right(3)+(3{)}^2]$
Using, $(a-b{)}^2=a^2-2ab+b^2$
$=x^2-(y-3{)}^2$
Using, $a^2-b^2=(a+b)(a-b)$
$=(x+y-3)[x-(y-3\left)\right]$
$=(x+y-3)(x-y+3)$

$\therefore x^2-y^2+6y-9=(x+y-3)(x-y+3).$