Question

Factorise the following using suitable identities:
$x^2-y^2+2x+1$

Answer 1

$x^2-y^2+2x+1$

$=(x^2+2x+1)-y^2$ using ${(a+b)}^2=a^2+2ab+b^2$

$={(x+1)}^2-y^2$

$=(x+1+y)(x+1-y)$ using $a^2-b^2=(a-b)(a+b)$

$=(x+y+1)(x-y+1)$