Question
Solve:
$ x^2-y^2-4 x z+4 z^2 $
$ x^2-y^2-4 x z+4 z^2 $
✓
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) $
$ =\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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