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Algebraic Identities

Factorize:aa-...

Question

Factorize:
a(a − 2b − c) + 2bc

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Solution

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

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