Factorize each of the following expression:

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

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

$=a(a-c)+b(a-c)$

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