Factorize by taking out the common factors:
$x^{3} (2 x - 3 y) - x^{2} (2 x - 3 y)^{2}$

x^{2} (2 x - 3 y) (3 y - x)

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x^{3} (x - 3 y) (y - x)

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x^{3} (x + 3 y) (3 y - x)

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x^{2} (2 x - y) (y + x)

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Solution

The correct option is A $x^{2} (2 x - 3 y) (3 y - x)$
$x^{3} (2 x - 3 y) - x^{2} (2 x - 3 y)^{2}$
$= x^{2} (2 x - 3 y) (x - (2 x - 3 y))$
$= x^{2} (2 x - 3 y) (x - 2 x + 3 y)$
$= x^{2} (2 x - 3 y) (3 y - x)$

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