Factorize each of the following expressions:

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

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

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

$=(x+b)(x-2 a)$        $[$ Taking $(x-2 a)$ as the common factor $]$

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