Factors of ${(2 x - 3 y)}^{3} + {(3 y - 5 z)}^{3} + {(5 z - 2 x)}^{3}$

3 (2 x - 3 y) (3 y - 5 z) (5 z - 2 x)

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3 (3 x - 2 y) (3 y - 5 z) (5 z - 2 x)

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3 (2 x - 3 y) (5 y - 3 z) (5 z - 2 x)

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3 (2 x - 3 y) (3 y - 5 z) (2 z - 5 x)

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Solution

The correct option is A $3 (2 x - 3 y) (3 y - 5 z) (5 z - 2 x)$
Since $(2 x - 3 y) + (3 y - 5 z) (5 z - 2 x) = 0$
${(2 x - 3 y)}^{3} + {(3 y - 5 z)}^{3} + {(5 z - 2 x)}^{3}$
$= 3 (2 x - 3 y) (3 y - 5 z) (5 z - 2 x)$

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