Question:
Factorize each of the following expression:
a(a − 2b − c) + 2bc
Solution:
$a(a-2 b-c)+2 b c=a^{2}-2 a b-a c+2 b c$
$=\left(a^{2}-a c\right)+(2 b c-2 a b)$ [Regrouping the terms]
$=a(a-c)+2 b(c-a)$
$=a(a-c)-2 b(a-c)$ $[\because(c-a)=-(a-c)]$
$=(a-2 b)(a-c)$ $[$ Taking $(a-c)$ as the common factor $]$
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