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Question
Simplify:
x2(x − y) y2(x + 2y)
Solution
To simplify, we will proceed as follows:
\[x^2 \left( x - y \right) y^2 \left( x + 2y \right)\]
\[ = \left[ x^2 \left( x - y \right) \right]\left[ y^2 \left( x + 2y \right) \right]\]
\[ = \left( x^3 - x^2 y \right)\left( x y^2 + 2 y^3 \right)\]
\[ = x^3 \left( x y^2 + 2 y^3 \right) - x^2 y\left( x y^2 + 2 y^3 \right)\]
\[ = x^4 y^2 + 2 x^3 y^3 - \left[ x^3 y^3 + 2 x^2 y^4 \right]\]
\[ = x^4 y^2 + 2 x^3 y^3 - x^3 y^3 - 2 x^2 y^4 \]
\[ = x^4 y^2 + x^3 y^3 - 2 x^2 y^4\]
Thus, the answer is \[x^4 y^2 + x^3 y^3 - 2 x^2 y^4\].
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