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Question
Simplify:
(x2 − 2y2) (x + 4y) x2y2
Solution
To simplify, we will proceed as follows:
\[\left( x^2 - 2 y^2 \right)\left( x + 4y \right) x^2 y^2 \]
\[ = \left[ x^2 \left( x + 4y \right) - 2 y^2 \left( x + 4y \right) \right] x^2 y^2 \]
\[ = \left( x^3 + 4 x^2 y - 2x y^2 - 8 y^3 \right) x^2 y^2 \]
\[ = x^5 y^2 + 4 x^4 y^3 - 2 x^3 y^4 - 8 x^2 y^5\]
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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