Question

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

Answer 1

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

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

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