Question:
Factorize each of the following algebraic expression:
9z2 − x2 + 4xy − 4y2
Solution:
$9 z^{2}-x^{2}+4 x y-4 y^{2}$
$=9 z^{2}-\left(x^{2}-4 x y+4 y^{2}\right)$
$=9 z^{2}-\left[x^{2}-2 \times x \times 2 y+(2 y)^{2}\right]$
$=(3 z)^{2}-(x-2 y)^{2}$
$=[3 z-(x-2 y)][3 z+(x-2 y)]$
$=(3 z-x+2 y)(3 z+x-2 y)$
$=(x-2 y+3 z)(-x+2 y+3 z)$
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