Question

Factorize:
$a^2+2ab+b^2-c^2$

Answer 1

Given: $a^2+2ab+b^2-c^2$

$\therefore a^2+2ab+b^2-c^2$
$=(a+b{)}^2-c^2$
$[\because x^2+y^2+2xy=(x+y{)}^2]$
$=(a+b+c)(a+b-c)$
$[\because x^2-y^2=(x+y\left)\right(x-y\left)\right]$

Hence, $a^2+2ab+b^2-c^2=(a+b+c)(a+b-c).$