Factorize each of the following algebraic expression:

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

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

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

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

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

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