Factorise: a^3+a b(1-2 a)-2 b^2 - Vidyadip

Question

Factorise:
$a^3+a b(1-2 a)-2 b^2$

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Answer

$a^3+a b(1-2 a)-2 b^2$
$=a^3+a b-2 a^2 b-2 b^2$
$=a\left(a^2+b\right)-2 b\left(a^2+b\right)$
$=\left(a^2+b\right)(a-2 b)$

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