Factorize:$x^2 – y^2 – 4xz + 4z^2$

Given :

$x^2 – y^2 – 4xz + 4z^2$

To do :

We have to factorize the given expression.

Solution :

$x^2 - y^2 - 4xz + 4z^2 = x^2 - 4xz + 4z^2 - y^2$

$= (x)^2 - 2 \times x \times 2z + (2z)^2 - (y)^2$

$= (x - 2z)^2 - (y)^2$

$= (x - 2z + y) (x - 2z - y)$

$= (x +y - 2z) (x - y - 2z)$

Hence, $x^2 - y^2 - 4xz + 4z^2 = (x +y - 2z) (x - y - 2z)$.

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Updated on: 10-Oct-2022

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