What is expand ((-1+r^3)^2)/(r^3) ?

The solution to expand ((-1+r^3)^2)/(r^3) is 1/(r^3)-2+r^3

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expand ((-1+r^3)^2)/(r^3)

expand

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

\frac{1}{r ^{3}} - 2 + r^{3}

Solution steps

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

(- 1 + r^{3})^{2} = 1 - 2 r^{3} + r^{6}

= \frac{1 - 2 r ^{3} + r ^{6}}{r ^{3}}

Apply the fraction rule:

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

\frac{1 - 2 r ^{3} + r ^{6}}{r ^{3}} = \frac{1}{r ^{3}} - \frac{2 r ^{3}}{r ^{3}} + \frac{r ^{6}}{r ^{3}}

= \frac{1}{r ^{3}} - \frac{2 r ^{3}}{r ^{3}} + \frac{r ^{6}}{r ^{3}}

Cancel

\frac{2 r ^{3}}{r ^{3}} : 2

= \frac{1}{r ^{3}} - 2 + \frac{r ^{6}}{r ^{3}}

Cancel

\frac{r ^{6}}{r ^{3}} : r^{3}

= \frac{1}{r ^{3}} - 2 + r^{3}

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