What is expand ((xy+6)^3)/(8y^3) ?

The solution to expand ((xy+6)^3)/(8y^3) is (x^3)/8+(9x^2)/(4y)+(27x)/(2y^2)+(27)/(y^3)

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expand ((xy+6)^3)/(8y^3)

expand

\frac{( x y + 6 ) ^{3}}{8 y ^{3}}

\frac{x ^{3}}{8} + \frac{9 x ^{2}}{4 y} + \frac{27 x}{2 y ^{2}} + \frac{27}{y ^{3}}

Solution steps

\frac{( x y + 6 ) ^{3}}{8 y ^{3}}

(x y + 6)^{3} = x^{3} y^{3} + 18 x^{2} y^{2} + 108 x y + 216

= \frac{x ^{3} y ^{3} + 18 x ^{2} y ^{2} + 108 x y + 216}{8 y ^{3}}

Apply the fraction rule:

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

\frac{x ^{3} y ^{3} + 18 x ^{2} y ^{2} + 108 x y + 216}{8 y ^{3}} = \frac{x ^{3} y ^{3}}{8 y ^{3}} + \frac{18 x ^{2} y ^{2}}{8 y ^{3}} + \frac{108 x y}{8 y ^{3}} + \frac{216}{8 y ^{3}}

= \frac{x ^{3} y ^{3}}{8 y ^{3}} + \frac{18 x ^{2} y ^{2}}{8 y ^{3}} + \frac{108 x y}{8 y ^{3}} + \frac{216}{8 y ^{3}}

\frac{x ^{3} y ^{3}}{8 y ^{3}} = \frac{x ^{3}}{8}

\frac{18 x ^{2} y ^{2}}{8 y ^{3}} = \frac{9 x ^{2}}{4 y}

\frac{108 x y}{8 y ^{3}} = \frac{27 x}{2 y ^{2}}

\frac{216}{8 y ^{3}} = \frac{27}{y ^{3}}

= \frac{x ^{3}}{8} + \frac{9 x ^{2}}{4 y} + \frac{27 x}{2 y ^{2}} + \frac{27}{y ^{3}}

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What is expand ((xy+6)^3)/(8y^3) ?
The solution to expand ((xy+6)^3)/(8y^3) is (x^3)/8+(9x^2)/(4y)+(27x)/(2y^2)+(27)/(y^3)