Factorise:

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

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

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

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

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