Factorize each of the following expression:

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

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

$=b x(a x-1)+y(a x-1)$

$=(b x+y)(a x-1)$           $[$ Taking $(a x-1)$ as the common factor $]$