$$ x^2- 2xy + y^2 -a^2 -2ab -b^2 $$
Above terms can be written as,
$$ (x^2 +2xy +y^2) -(a^2 +2ab+b^2) $$
We know that $$ (a+b)^2 = a^2 +2ab +b^2 $$ and $$ (a-b)^2 = a^2 -2ab +b^2 $$
$$ (x^2 -( 2 \times x \times y) + y^2) - (a^2 + ( 2 \times a \times b) +b^2 ) $$
$$ (x-y)^2 -(a+b)^2 $$
We know that , $$ a^2 - b^2 =(a+b)(a-b) $$
$$ [ (x-y) +(a+b)] [(x-y) -(a+b) ] $$
$$ ( x-y +a+b)(x-y -a-b) $$