Question
Fill in the blanks.
$9 z^2-x^2-4 y^2+4 x y$=(_______)(_______)
$9 z^2-x^2-4 y^2+4 x y$=(_______)(_______)
✓
Answer
$(3z + x - 2y)(3z - x + 2y)$
Solution:
$ 9 z^2-x^2-4 y^2+4 x y $
$ =9 z^2-\left(x^2-4 x y+4 y^2\right) $
$=9 z^2-\left(x^2-2 \times x \times 2 y+(2 y)^2\right)$
$ =9 z^2-(x-2 y)^2$
$ =(3 z)^2-(x-2 y)^2$
$=(3 z+(x-2 y))(3 z-(x-2 y))$
$ =(3 z+x-2 y)(3 z-x+2 y)$
Solution:
$ 9 z^2-x^2-4 y^2+4 x y $
$ =9 z^2-\left(x^2-4 x y+4 y^2\right) $
$=9 z^2-\left(x^2-2 \times x \times 2 y+(2 y)^2\right)$
$ =9 z^2-(x-2 y)^2$
$ =(3 z)^2-(x-2 y)^2$
$=(3 z+(x-2 y))(3 z-(x-2 y))$
$ =(3 z+x-2 y)(3 z-x+2 y)$
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