Factorize each of the following algebraic expression:

$x^{2}-y^{2}+6 y-9$

$=x^{2}-\left(y^{2}-6 y+9\right)$

$=x^{2}-\left(y^{2}-2 \times y \times 3+3^{2}\right)$

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

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

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