Simplify: ${(3 x + 4 y)}^{3} - {(3 x - 4 y)}^{3} - 216 x^{2} y$

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Solution

simplify $:$ ${(3 x + 4 y)}^{3} - {(3 x - 4 y)}^{3} - 216 x^{2} y$
We know $:$ ${(a + b)}^{3} = a^{3} + b^{3} + 3 a^{2} b + 3 a b^{2}$
And ${(a - b)}^{3} = a^{3} - b^{3} - 3 a^{2} b + 3 a b^{2}$
So $,$
$\Rightarrow 27 x^{3} + 64 y^{3} + 108 x^{2} y + 144 x y^{2} - (27 x^{3} - 64 y^{3} - 108 x^{2} y + 144 x y^{2}) - 216 x^{2} y$
$\Rightarrow 128 y^{3} + 216 x^{2} y - 216 x^{2} y$
$\Rightarrow 128 y^{3}$ Answer.

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