Simplify: 4 a b(a-b)-6 a^2 (b-b^2 )-3 b^2 (2 a^2-a )+2 a b(b-a)

Question

Simplify:
$4 a b(a-b)-6 a^2\left(b-b^2\right)-3 b^2\left(2 a^2-a\right)+2 a b(b-a)$

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Answer

To simplify, we will use distributive law as follows:
$4 a b(a-b)-6 a^2\left(b-b^2\right)-3 b^2\left(2 a^2-a\right)+2 a b(b-a)$
$=4 a^2 b-4 a b^2-6 a^2 b+6 a^2 b^2-6 b^2 a^2+3 b^2 a+2 a b^2-2 a^2 b$
$=4 a^2 b-6 a^2 b-2 a^2 b-4 a b^2+3 b^2 a+2 a b^2+6 a^2 b^2-6 b^2 a^2$
$=-4 a^2 b+a b^2$

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