Find the value

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

Using the identity $(a-b)^{2}=a^{2}+b^{2}-2 a b$

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

Using the identity $a^{2}-b^{2}=(a+b)(a-b)$

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

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

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