Factorize each of the following algebraic expression:

$a^{2}-2 a b+b^{2}-c^{2}$

$=\left(a^{2}-2 a b+b^{2}\right)-c^{2}$

$=\left(a^{2}-2 \times a \times b+b^{2}\right)-c^{2}$

$=(a-b)^{2}-c^{2}$

$=[(a-b)-c][(a-b)+c]$

$=(a-b-c)(a-b+c)$