What is expand ((-z-1)^3z)/6 ?

The solution to expand ((-z-1)^3z)/6 is -(z^4)/6-(z^3)/2-(z^2)/2-z/6

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expand ((-z-1)^3z)/6

expand

\frac{( - z - 1 ) ^{3} z}{6}

- \frac{z ^{4}}{6} - \frac{z ^{3}}{2} - \frac{z ^{2}}{2} - \frac{z}{6}

Solution steps

\frac{( - z - 1 ) ^{3} z}{6}

(- z - 1)^{3} = - z^{3} - 3 z^{2} - 3 z - 1

= \frac{z ( - z ^{3} - 3 z ^{2} - 3 z - 1 )}{6}

Expand

(- z^{3} - 3 z^{2} - 3 z - 1) z : - z^{4} - 3 z^{3} - 3 z^{2} - z

= \frac{- z ^{4} - 3 z ^{3} - 3 z ^{2} - z}{6}

Apply the fraction rule:

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

\frac{- z ^{4} - 3 z ^{3} - 3 z ^{2} - z}{6} = - \frac{z ^{4}}{6} - \frac{3 z ^{3}}{6} - \frac{3 z ^{2}}{6} - \frac{z}{6}

= - \frac{z ^{4}}{6} - \frac{3 z ^{3}}{6} - \frac{3 z ^{2}}{6} - \frac{z}{6}

Cancel

\frac{3 z ^{3}}{6} : \frac{z ^{3}}{2}

= - \frac{z ^{4}}{6} - \frac{z ^{3}}{2} - \frac{3 z ^{2}}{6} - \frac{z}{6}

Cancel

\frac{3 z ^{2}}{6} : \frac{z ^{2}}{2}

= - \frac{z ^{4}}{6} - \frac{z ^{3}}{2} - \frac{z ^{2}}{2} - \frac{z}{6}

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What is expand ((-z-1)^3z)/6 ?
The solution to expand ((-z-1)^3z)/6 is -(z^4)/6-(z^3)/2-(z^2)/2-z/6