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}

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}

(t + a)^{2} + e^{- a t} - 2 cos (a t)

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

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

\frac{3 x ^{2} - 10 x - 5}{( x - 1 ) ^{2} ( x + 2 )}

(5 - 2) (4 + 3)

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