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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