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}

3 (8 + Δ x)^{2}

5 (\frac{448}{3} + 2 ln (\frac{253}{29}))

10 (\frac{125}{2} e^{- x} - \frac{125}{2} e^{- 5 x})

- \frac{2}{5} (26.74 + z) - \frac{2}{5} (26, 26 + z) + \frac{2}{25}

(11 k^{7} m^{4} + 76 d^{4} e^{7}) (11 k^{7} m^{4} - 76 d^{4} e^{7})

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