Simplify: a^2 b (a-b^2 )+a b^2 (4 a b-2 a^2 )-a^3 b(1-2 b)

Question

Simplify:
$a^2 b\left(a-b^2\right)+a b^2\left(4 a b-2 a^2\right)-a^3 b(1-2 b)$

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Answer

To simplify, we will use distributive law as follows:
$a^2 b\left(a-b^2\right)+a b^2\left(4 a b-2 a^2\right)-a^3 b(1-2 b)$
$=a^3 b-a^2 b^3+4 a^2 b^3-2 a^3 b^2-a^3 b+2 a^3 b^2$
$=a^3 b-a^3 b-a^2 b^3+4 a^2 b^3-2 a^3 b^2+2 a^3 b^2$
$=3 a^2 b^3$

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