Solve:x^2-y^2-4 x z+4 z^2 - Vidyadip

Question

Solve:$x^2-y^2-4 x z+4 z^2$

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Answer

$x^2-y^2-4 x z+4 z^2=\left(x^2-4 x z+4 z^2\right)-y^2$
$=(x-2 z)^2-y^2$
$=[(x-2 z)-y][(x-2 z)+y)]$
$=(x-2 z-y)(x-2 z+y)$
$=(x+y-2 z)(x-y-2 z)$

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