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Question
Simplify:
x2(x + 2y) (x − 3y)
Solution
To simplify, we will proceed as follows:
\[x^2 \left( x + 2y \right)\left( x - 3y \right)\]
\[ = \left[ x^2 \left( x + 2y \right) \right]\left( x - 3y \right)\]
\[ = \left( x^3 + 2 x^2 y \right)\left( x - 3y \right)\]
\[ = x^3 \left( x - 3y \right) + 2 x^2 y\left( x - 3y \right)\]
\[ = x^4 - 3 x^3 y + 2 x^3 y - 6 x^2 y^2 \]
\[ = x^4 - x^3 y - 6 x^2 y^2\]
Thus, the answer is \[x^4 - x^3 y - 6 x^2 y^2\].
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