Question
Simplify:
$ (a-b)\left(a^2+b^2+a b\right)-(a+b)\left(a^2+b^2-a b\right) $
$ (a-b)\left(a^2+b^2+a b\right)-(a+b)\left(a^2+b^2-a b\right) $
✓
Answer
$(a-b)\left(a^2+b^2+a b\right)-(a+b)\left(a^2+b^2-a b\right) $
$ =a\left(a^2+b^2+a b\right)-b\left(a^2+b^2+a b\right)-a\left(a^2+b^2-a b\right)-b\left(a^2+b^2-a b\right) $
$ =a^3+a b^2+a^2 b-b a^2-b^3-a b^2-a^3-a b^2+a^2 b-b a^2-b^3+a b^2 $
$ =\left(a^3-a^3\right)+\left(-b^3-b^3\right)+\left(a b^2-a b^2\right)+\left(a^2 b-a^2 b+a^2 b-a^2 b\right) $
$ =0-2 b^3+0+0+0 $
$ =-2 b^3$
$ =a\left(a^2+b^2+a b\right)-b\left(a^2+b^2+a b\right)-a\left(a^2+b^2-a b\right)-b\left(a^2+b^2-a b\right) $
$ =a^3+a b^2+a^2 b-b a^2-b^3-a b^2-a^3-a b^2+a^2 b-b a^2-b^3+a b^2 $
$ =\left(a^3-a^3\right)+\left(-b^3-b^3\right)+\left(a b^2-a b^2\right)+\left(a^2 b-a^2 b+a^2 b-a^2 b\right) $
$ =0-2 b^3+0+0+0 $
$ =-2 b^3$
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