Factorize each of the following algebraic expression:

$9 z^{2}-x^{2}+4 x y-4 y^{2}$

$=9 z^{2}-\left(x^{2}-4 x y+4 y^{2}\right)$

$=9 z^{2}-\left[x^{2}-2 \times x \times 2 y+(2 y)^{2}\right]$

$=(3 z)^{2}-(x-2 y)^{2}$

$=[3 z-(x-2 y)][3 z+(x-2 y)]$

$=(3 z-x+2 y)(3 z+x-2 y)$

$=(x-2 y+3 z)(-x+2 y+3 z)$