Question

Simplify:
(x² − 2y²) (x + 4y) x²y²

Answer 1

To simplify, we will proceed as follows:

$$\begin{gathered} \left(x^2-2y^2\right)\left(x+4y\right)x^2{y}^2 \\ =\left[x^2\left(x+4y\right)-2y^2\left(x+4y\right)\right]x^2{y}^2 \\ =\left(x^3+4x^{2}y-2x{y}^2-8y^3\right)x^2{y}^2 \\ =x^5{y}^2+4x^4{y}^3-2x^3{y}^4-8x^2{y}^5 \end{gathered}$$

Thus, the answer is $x^5{y}^2+4x^4{y}^3-2x^3{y}^4-8x^2{y}^5$.