Factorize each of the following expression:

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

$=(x-y)+\left(y^{2}-x^{2}\right)$      [Regrouping the terms]

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

$=(x-y)-(y+x)(x-y)$                          $[\because(y-x)=-(x-y)]$

$=(x-y)[1-(y+x)]$

$=(x-y)(1-x-y)$