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

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

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

expand

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

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

Solution steps

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

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

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

Apply the fraction rule:

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

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

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

Cancel

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

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

Cancel

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

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

Cancel

\frac{3 y}{y} : 3

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

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

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