What is expand (x*(x-1)*(x-2))/6 ?

The solution to expand (x*(x-1)*(x-2))/6 is (x^3)/6-(x^2)/2+x/3

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expand (x(x-1)(x-2))/6

expand

\frac{x \cdot ( x - 1 ) \cdot ( x - 2 )}{6}

\frac{x ^{3}}{6} - \frac{x ^{2}}{2} + \frac{x}{3}

Solution steps

\frac{x ( x - 1 ) ( x - 2 )}{6}

Expand

x (x - 1) (x - 2) : x^{3} - 3 x^{2} + 2 x

= \frac{x ^{3} - 3 x ^{2} + 2 x}{6}

Apply the fraction rule:

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

\frac{x ^{3} - 3 x ^{2} + 2 x}{6} = \frac{x ^{3}}{6} - \frac{3 x ^{2}}{6} + \frac{2 x}{6}

= \frac{x ^{3}}{6} - \frac{3 x ^{2}}{6} + \frac{2 x}{6}

Cancel

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

= \frac{x ^{3}}{6} - \frac{x ^{2}}{2} + \frac{2 x}{6}

Cancel

\frac{2 x}{6} : \frac{x}{3}

= \frac{x ^{3}}{6} - \frac{x ^{2}}{2} + \frac{x}{3}

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What is expand (x*(x-1)*(x-2))/6 ?
The solution to expand (x*(x-1)*(x-2))/6 is (x^3)/6-(x^2)/2+x/3