Simplify $x^{2} (x - 3 y^{2}) - x y (y^{2} - 2 x y) - x (y^{3} - 5 x^{2})$

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Solution

Given $x^{2} (x - 3 y^{2}) - x y (y^{2} - 2 x y) - x (y^{3} - 5 x^{2})$

$= x^{3} - 3 x^{2} y^{2} - x y^{3} + 2 x^{2} y^{2} - x y^{3} + 5 x^{3}$

$= 6 x^{3} - 2 x y^{3} - x^{2} y^{2}$

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