Question
Solve:
$ 9 z^2-x^2+4 x y-4 y^2 $
$ 9 z^2-x^2+4 x y-4 y^2 $
✓
Answer
$ 9 z^2-x^2+4 x y-4 y^2 $
$ =9 z^2-\left(x^2-4 x y+4 y^2\right) $
$ =9 z^2-\left[x^2-2 x \times 2 y+(2 y)^2\right] $
$ =(3 z)^2-(x-2 y)^2 $
$ =[3 z-(x-2 y)][3 z+(x-2 y) $
$ =(3 z-x+2 y)(3 x+x-2 y) $
$ =(x-2 y+3 z)(-x+2 y+3 z) $
$ =9 z^2-\left(x^2-4 x y+4 y^2\right) $
$ =9 z^2-\left[x^2-2 x \times 2 y+(2 y)^2\right] $
$ =(3 z)^2-(x-2 y)^2 $
$ =[3 z-(x-2 y)][3 z+(x-2 y) $
$ =(3 z-x+2 y)(3 x+x-2 y) $
$ =(x-2 y+3 z)(-x+2 y+3 z) $
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