What is expand-((x+y)^2y-y)/x ?

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

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expand-((x+y)^2y-y)/x

expand

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

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

Solution steps

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

(x + y)^{2} = x^{2} + 2 x y + y^{2}

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

Expand

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

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

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

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

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

Remove parentheses:

(a) = a, - (- a) = a

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

Cancel

\frac{x ^{2} y}{x} : x y

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

Cancel

\frac{2 x y ^{2}}{x} : 2 y^{2}

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

\frac{5 s + 13}{s ( s ^{2} + 4 s + 13 )}

\frac{( x y - x ) x}{y ( y x - y )}

(9 ab c^{3}) (14 b c^{2})

\frac{( x - i y ) ^{2}}{x ^{2} + y ^{2}}

e^{2 (x + y i)}

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