What is expand (2x(-x^4+y^4)^2)/(y^9) ?

The solution to expand (2x(-x^4+y^4)^2)/(y^9) is (2x^9}{y^9}-(4x^5)/(y^5)+\frac{2x)/y

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expand (2x(-x^4+y^4)^2)/(y^9)

expand

\frac{2 x ( - x ^{4} + y ^{4} ) ^{2}}{y ^{9}}

\frac{2 x ^{9}}{y ^{9}} - \frac{4 x ^{5}}{y ^{5}} + \frac{2 x}{y}

Solution steps

\frac{2 x ( - x ^{4} + y ^{4} ) ^{2}}{y ^{9}}

(- x^{4} + y^{4})^{2} = x^{8} - 2 x^{4} y^{4} + y^{8}

= \frac{2 x ( x ^{8} - 2 x ^{4} y ^{4} + y ^{8} )}{y ^{9}}

Expand

2 x (x^{8} - 2 x^{4} y^{4} + y^{8}) : 2 x^{9} - 4 x^{5} y^{4} + 2 x y^{8}

= \frac{2 x ^{9} - 4 x ^{5} y ^{4} + 2 x y ^{8}}{y ^{9}}

Apply the fraction rule:

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

\frac{2 x ^{9} - 4 x ^{5} y ^{4} + 2 x y ^{8}}{y ^{9}} = \frac{2 x ^{9}}{y ^{9}} - \frac{4 x ^{5} y ^{4}}{y ^{9}} + \frac{2 x y ^{8}}{y ^{9}}

= \frac{2 x ^{9}}{y ^{9}} - \frac{4 x ^{5} y ^{4}}{y ^{9}} + \frac{2 x y ^{8}}{y ^{9}}

Cancel

\frac{4 x ^{5} y ^{4}}{y ^{9}} : \frac{4 x ^{5}}{y ^{5}}

= \frac{2 x ^{9}}{y ^{9}} - \frac{4 x ^{5}}{y ^{5}} + \frac{2 x y ^{8}}{y ^{9}}

Cancel

\frac{2 x y ^{8}}{y ^{9}} : \frac{2 x}{y}

= \frac{2 x ^{9}}{y ^{9}} - \frac{4 x ^{5}}{y ^{5}} + \frac{2 x}{y}

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What is expand (2x(-x^4+y^4)^2)/(y^9) ?
The solution to expand (2x(-x^4+y^4)^2)/(y^9) is (2x^9}{y^9}-(4x^5)/(y^5)+\frac{2x)/y