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) $
✓
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 $
$ 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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