Question
Factorize of the following expressions:
$a(a-2 b-c)+2 b c$
$a(a-2 b-c)+2 b c$
✓
Answer
$a(a-2 b-c)+2 b c=a^2-2 a b-a c+2 b c$
$=\left(a^2-a c\right)+(2 b c-2 a b)$
$=a(a-c)+2 b(c-a)[\text { since, } 9 c-a)=-(a-c)]$
$=a(a-c)-2 b(a-c)$
$=(a-2 b)(a-c)[\text { taking }(a-c) \text { as the common factor] }$
$=\left(a^2-a c\right)+(2 b c-2 a b)$
$=a(a-c)+2 b(c-a)[\text { since, } 9 c-a)=-(a-c)]$
$=a(a-c)-2 b(a-c)$
$=(a-2 b)(a-c)[\text { taking }(a-c) \text { as the common factor] }$
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