What is expand (-1+x/y)^3 ?

The solution to expand (-1+x/y)^3 is (-y^3+3xy^2+x^3-3x^2y)/(y^3)

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expand (-1+x/y)^3

expand

(- 1 + \frac{x}{y})^{3}

\frac{- y ^{3} + 3 x y ^{2} + x ^{3} - 3 x ^{2} y}{y ^{3}}

Solution steps

(- 1 + \frac{x}{y})^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(- 1 + \frac{x}{y})^{3} = (- 1)^{3} + 3 (- 1)^{2} \frac{x}{y} + 3 (- 1) (\frac{x}{y})^{2} + (\frac{x}{y})^{3}

= (- 1)^{3} + 3 (- 1)^{2} \frac{x}{y} + 3 (- 1) (\frac{x}{y})^{2} + (\frac{x}{y})^{3}

Simplify

(- 1)^{3} + 3 (- 1)^{2} \frac{x}{y} + 3 (- 1) (\frac{x}{y})^{2} + (\frac{x}{y})^{3} : \frac{- y ^{3} + 3 x y ^{2} + x ^{3} - 3 x ^{2} y}{y ^{3}}

= \frac{- y ^{3} + 3 x y ^{2} + x ^{3} - 3 x ^{2} y}{y ^{3}}

(1 + \frac{x}{2}) (2 - 3 x)^{6}

e^{2 x} (a cos (5 x) + b sin (5 x))

\frac{x + 8}{x ( x + 2 )}

\frac{\partial}{\partial x} ((y) (y^{5} - 3 x y))

\frac{5 ( 1 + 3 cos ( x ) )}{( 3 + cos ( x ) ) ^{2}}

What is expand (-1+x/y)^3 ?
The solution to expand (-1+x/y)^3 is (-y^3+3xy^2+x^3-3x^2y)/(y^3)