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

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

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x^{2} (2 x - 3 y) (3 y - 7 x)

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

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

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Solution

The correct option is B $x^{2} (2 x - 3 y) (3 y - x)$
$x^{3} (2 x - 3 y) - x^{2} {(2 x - 3 y)}^{2}$
$= x^{2} (2 x - 3 y) [x - (2 x - 3 y)]$
$= x^{2} (2 x - 3 y) (3 y - x)$

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