Factorize each of the following algebraic expressions:

$a(x-y)+2 b(y-x)+c(x-y)^{2}$

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

$=[a-2 b+c(x-y)](x-y)$

$=(a-2 b+c x-c y)(x-y)$