Simplify: x^2(x-y) y^2(x+2 y) - Vidyadip

Question

Simplify:
$x^2(x-y) y^2(x+2 y)$

✓

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 $x^4 y^2+x^3 y^3-2 x^2 y^4$.

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