What is expand ((x+3)^4)/4 ?

The solution to expand ((x+3)^4)/4 is (x^4)/4+3x^3+(27x^2)/2+27x+81/4

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expand ((x+3)^4)/4

expand

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

\frac{x ^{4}}{4} + 3 x^{3} + \frac{27 x ^{2}}{2} + 27 x + \frac{81}{4}

Solution steps

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

(x + 3)^{4} = x^{4} + 12 x^{3} + 54 x^{2} + 108 x + 81

= \frac{x ^{4} + 12 x ^{3} + 54 x ^{2} + 108 x + 81}{4}

Apply the fraction rule:

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

\frac{x ^{4} + 12 x ^{3} + 54 x ^{2} + 108 x + 81}{4} = \frac{x ^{4}}{4} + \frac{12 x ^{3}}{4} + \frac{54 x ^{2}}{4} + \frac{108 x}{4} + \frac{81}{4}

= \frac{x ^{4}}{4} + \frac{12 x ^{3}}{4} + \frac{54 x ^{2}}{4} + \frac{108 x}{4} + \frac{81}{4}

Divide the numbers:

\frac{12}{4} = 3

= \frac{x ^{4}}{4} + 3 x^{3} + \frac{54 x ^{2}}{4} + \frac{108 x}{4} + \frac{81}{4}

Cancel

\frac{54 x ^{2}}{4} : \frac{27 x ^{2}}{2}

= \frac{x ^{4}}{4} + 3 x^{3} + \frac{27 x ^{2}}{2} + \frac{108 x}{4} + \frac{81}{4}

Divide the numbers:

\frac{108}{4} = 27

= \frac{x ^{4}}{4} + 3 x^{3} + \frac{27 x ^{2}}{2} + 27 x + \frac{81}{4}

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

10 x (2 - ln (x))

\frac{5 ( 9 - 201 )}{3}

l (t - 1) 2 e^{3} t

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

What is expand ((x+3)^4)/4 ?
The solution to expand ((x+3)^4)/4 is (x^4)/4+3x^3+(27x^2)/2+27x+81/4