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

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- 18 y (4 x^{2} + 3 y^{2})

18 y (4 x^{2} + 3 y^{2})

18 y (4 x^{2} - 3 y^{2})

18 y (2 x^{2} + 9 y^{2})

answer is A.

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Detailed Solution

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

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

$= (6 y) (4 x^{2} + 9 y^{2} + 12 x y + 4 x^{2} - 9 y^{2} + 4 x^{2} + 9 y^{2} - 12 x y)$

$= (6 y) (12 x^{2} + 9 y^{2})$

$= 18 y (4 x^{2} + 3 y^{2})$

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