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)$
$ 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)$
✓
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)$
$=4 a^2 b-4 a b^2-6 a^2 b+6 a^2 b^2-6 b^2 a^2+3 b^2 a+2 a b^2-2 a^2 b$
$=4 a^2 b-6 a^2 b- 2 a^2 b-4 a b^2+3 b^2 a+2 a b^2+6 a^2 b^2-6 b^2 a^2$
$=-4 a^2 b+a b^2$
$ 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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