Factorise:

$x^{2}+2 x y+y^{2}-a^{2}+2 a b-b^{2}$

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

$=(x+y)^{2}-(a-b)^{2} \quad\left[a^{2}+2 a b+b^{2}=(a+b)^{2}\right.$ and $\left.a^{2}-2 a b+b^{2}=(a-b)^{2}\right]$

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

$=(x+y+a-b)(x+y-a+b)$