Expand $(- y + 3 x)^{3}$

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Solution

$(- y + 3 x)^{3} = (- y)^{3} + (3 x)^{3} + 3 (- y) (3 x) (- y + 3 x)$
Using, $(a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b)$
$= - y^{3} + 27 x^{3} - 9 x y (- y + 3 x)$
$= - y^{3} + 27 x^{3} + 9 y^{2} x - 27 y x^{2}$

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