Factorize: $x^{3} (2 x - 3 y) - x^{2} (2 x - 3 y)^{2}$

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

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

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

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x (2 x - 3 y) (3 y - x)

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Solution

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

$Taking out x^{2} (2 x - 3 y) as common term.$

$\Rightarrow x^{2} (2 x - 3 y) (\frac{x^{3} (2 x - 3 y)}{x^{2} (2 x - 3 y)} - \frac{x^{2} (2 x - 3 y)^{2}}{x^{2} (2 x - 3 y)})$

$\Rightarrow x^{2} (2 x - 3 y) (x - (2 x - 3 y))$

$\Rightarrow x^{2} (2 x - 3 y) (x - 2 x + 3 y))$

$\Rightarrow x^{2} (2 x - 3 y) (- x + 3 y))$

$\Rightarrow x^{2} (2 x - 3 y) (3 y - x)$

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Similar questions

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

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

Factorize the given expression:

$9 (2 x - 3 y)^{2} - 12 (2 x - 3 y) (2 x + 3 y) + 4 (2 x + 3 y)^{2}$

Factorization:

$9 (2 x - 3 y)^{2} - 12 (2 x - 3 y) (2 x + 3 y) + 4 (2 x + 3 y)^{2}$

(2 x + 3 y)^{2} - 12 x - 18 y - 7

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