Factorize:
$a(a+b-c)-b c$
We have:
$a(a+b-c)-b c=a^{2}+a b-a c-b c$
$=\left(a^{2}-a c\right)+(a b-b c)$
$=a(a-c)+b(a-c)$
$=(a-c)(a+b)$
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