What is expand-((-x+1)^4)/4 ?

The solution to expand-((-x+1)^4)/4 is -(x^4)/4+x^3-(3x^2)/2+x-1/4

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expand-((-x+1)^4)/4

expand

- \frac{( - x + 1 ) ^{4}}{4}

- \frac{x ^{4}}{4} + x^{3} - \frac{3 x ^{2}}{2} + x - \frac{1}{4}

Solution steps

- \frac{( - x + 1 ) ^{4}}{4}

(- x + 1)^{4} = x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1

= - \frac{x ^{4} - 4 x ^{3} + 6 x ^{2} - 4 x + 1}{4}

Apply the fraction rule:

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

\frac{x ^{4} - 4 x ^{3} + 6 x ^{2} - 4 x + 1}{4} = - (\frac{x ^{4}}{4}) - (- \frac{4 x ^{3}}{4}) - (\frac{6 x ^{2}}{4}) - (- \frac{4 x}{4}) - (\frac{1}{4})

= - (\frac{x ^{4}}{4}) - (- \frac{4 x ^{3}}{4}) - (\frac{6 x ^{2}}{4}) - (- \frac{4 x}{4}) - (\frac{1}{4})

Remove parentheses:

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

= - \frac{x ^{4}}{4} + \frac{4 x ^{3}}{4} - \frac{6 x ^{2}}{4} + \frac{4 x}{4} - \frac{1}{4}

Divide the numbers:

\frac{4}{4} = 1

= - \frac{x ^{4}}{4} + x^{3} - \frac{6 x ^{2}}{4} + \frac{4 x}{4} - \frac{1}{4}

Cancel

\frac{6 x ^{2}}{4} : \frac{3 x ^{2}}{2}

= - \frac{x ^{4}}{4} + x^{3} - \frac{3 x ^{2}}{2} + \frac{4 x}{4} - \frac{1}{4}

Divide the numbers:

\frac{4}{4} = 1

= - \frac{x ^{4}}{4} + x^{3} - \frac{3 x ^{2}}{2} + x - \frac{1}{4}

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