Question
Simplify:
$\left(x^2-2 y^2\right)(x+4 y) x^2 y^2$
$\left(x^2-2 y^2\right)(x+4 y) x^2 y^2$
✓
Answer
To simplify, we will proceed as follows:
$\left(x^2-2 y^2\right)(x+4 y) x^2 y^2$
$=\left[x^2(x+4 y)-2 y^2(x+4 y)\right] x^2 y^2$
$=\left(x^3+4 x^2 y-2 x y^2-8 y^3\right) x^2 y^2$
$=x^5 y^2+4 x^4 y^3-2 x^3 y^4-8 x^2 y^5$
Thus, the answer is $x^5 y^2+4 x^4 y^3-2 x^3 y^4-8 x^2 y^5$.
$\left(x^2-2 y^2\right)(x+4 y) x^2 y^2$
$=\left[x^2(x+4 y)-2 y^2(x+4 y)\right] x^2 y^2$
$=\left(x^3+4 x^2 y-2 x y^2-8 y^3\right) x^2 y^2$
$=x^5 y^2+4 x^4 y^3-2 x^3 y^4-8 x^2 y^5$
Thus, the answer is $x^5 y^2+4 x^4 y^3-2 x^3 y^4-8 x^2 y^5$.
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