Factorize:
Question:

Factorize:

$a^{3}+a b(1-2 a)-2 b^{2}$

 

Solution:

We have:

$a^{3}+a b(1-2 a)-2 b^{2}=a^{3}+a b-2 a^{2} b-2 b^{2}$

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

$=a^{2}(a-2 b)+b(a-2 b)$

$=(a-2 b)\left(a^{2}+b\right)$

 

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