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

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

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

expand

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

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

Solution steps

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

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{4}{4} = 1

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

Cancel

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

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

Divide the numbers:

\frac{4}{4} = 1

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

Rewrite in standard form

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

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

\frac{7}{( 4 + x ) ^{3}}

e^{2 t} t^{\frac{1}{5}} + t u (t - 4)

cot (a) (sin (a) + tan (a))

\frac{2 ( s ^{2} + 1 )}{s ^{2} ( s ^{2} + 5 )}

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