What is expand ((x-0)(x-1)(x-2)(x-6))/(-60) ?

The solution to expand ((x-0)(x-1)(x-2)(x-6))/(-60) is -(x^4}{60}+(3x^3)/(20)-\frac{x^2)/3+x/5

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expand ((x-0)(x-1)(x-2)(x-6))/(-60)

expand

\frac{( x - 0 ) ( x - 1 ) ( x - 2 ) ( x - 6 )}{- 60}

- \frac{x ^{4}}{60} + \frac{3 x ^{3}}{20} - \frac{x ^{2}}{3} + \frac{x}{5}

Solution steps

\frac{( x - 0 ) ( x - 1 ) ( x - 2 ) ( x - 6 )}{- 60}

x - 0 = x

= \frac{x ( x - 1 ) ( x - 2 ) ( x - 6 )}{- 60}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{x ( x - 1 ) ( x - 2 ) ( x - 6 )}{60}

Expand

x (x - 1) (x - 2) (x - 6) : x^{4} - 9 x^{3} + 20 x^{2} - 12 x

= - \frac{x ^{4} - 9 x ^{3} + 20 x ^{2} - 12 x}{60}

Apply the fraction rule:

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

\frac{x ^{4} - 9 x ^{3} + 20 x ^{2} - 12 x}{60} = - (\frac{x ^{4}}{60}) - (- \frac{9 x ^{3}}{60}) - (\frac{20 x ^{2}}{60}) - (- \frac{12 x}{60})

= - (\frac{x ^{4}}{60}) - (- \frac{9 x ^{3}}{60}) - (\frac{20 x ^{2}}{60}) - (- \frac{12 x}{60})

Remove parentheses:

(a) = a, - (- a) = a

= - \frac{x ^{4}}{60} + \frac{9 x ^{3}}{60} - \frac{20 x ^{2}}{60} + \frac{12 x}{60}

Cancel

\frac{9 x ^{3}}{60} : \frac{3 x ^{3}}{20}

= - \frac{x ^{4}}{60} + \frac{3 x ^{3}}{20} - \frac{20 x ^{2}}{60} + \frac{12 x}{60}

Cancel

\frac{20 x ^{2}}{60} : \frac{x ^{2}}{3}

= - \frac{x ^{4}}{60} + \frac{3 x ^{3}}{20} - \frac{x ^{2}}{3} + \frac{12 x}{60}

Cancel

\frac{12 x}{60} : \frac{x}{5}

= - \frac{x ^{4}}{60} + \frac{3 x ^{3}}{20} - \frac{x ^{2}}{3} + \frac{x}{5}

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What is expand ((x-0)(x-1)(x-2)(x-6))/(-60) ?
The solution to expand ((x-0)(x-1)(x-2)(x-6))/(-60) is -(x^4}{60}+(3x^3)/(20)-\frac{x^2)/3+x/5