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

Given :

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

To do :

We have to factorize the given expression.

Solution :

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

$= a^2 - (b - c)^2$

$= (a)^2 - (b - c)^2$

$= (a + b - c) [a - (b - c)]$

$= (a + b - c) (a - b + c)$

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

Tutorialspoint

Updated on: 10-Oct-2022

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