Question
Simplify:
$ x^2(x-y) y^2(x+2 y) $
$ x^2(x-y) y^2(x+2 y) $
✓
Answer
To simplify, we will proceed as follows:
$ x^2(x-y) y^2(x+2 y) $
$ =\left[x^2(x-y)\right]\left[y^2(x+2 y)\right] $
$ =\left(x^3-x^2 y\right)\left(x y^2+2 y^3\right) $
$ =x^3\left(x y^2+2 y^3\right)-x^2 y\left(x y^2+2 y^3\right) $
$ =x^4 y^2+2 x^3 y^3-\left[x^3 y^3+2 x^2 y^4\right] $
$ =x^4 y^2+2 x^3 y^3-x^3 y^3-2 x^2 y^4 $
$ =x^4 y^2+x^3 y^3-2 x^2 y^4$
Thus, the answer is $x^4 y^2+x^3 y^3-2 x^2 y^4$.
$ x^2(x-y) y^2(x+2 y) $
$ =\left[x^2(x-y)\right]\left[y^2(x+2 y)\right] $
$ =\left(x^3-x^2 y\right)\left(x y^2+2 y^3\right) $
$ =x^3\left(x y^2+2 y^3\right)-x^2 y\left(x y^2+2 y^3\right) $
$ =x^4 y^2+2 x^3 y^3-\left[x^3 y^3+2 x^2 y^4\right] $
$ =x^4 y^2+2 x^3 y^3-x^3 y^3-2 x^2 y^4 $
$ =x^4 y^2+x^3 y^3-2 x^2 y^4$
Thus, the answer is $x^4 y^2+x^3 y^3-2 x^2 y^4$.
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