What is expand ((v-1)^3)/v ?

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

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expand ((v-1)^3)/v

expand

\frac{( v - 1 ) ^{3}}{v}

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

Solution steps

\frac{( v - 1 ) ^{3}}{v}

(v - 1)^{3} = v^{3} - 3 v^{2} + 3 v - 1

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

Apply the fraction rule:

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

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

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

Cancel

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

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

Cancel

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

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

Cancel

\frac{3 v}{v} : 3

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

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