What is expand ((x^3+6)^4)/4 ?

The solution to expand ((x^3+6)^4)/4 is (x^{12})/4+6x^9+54x^6+216x^3+324

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expand ((x^3+6)^4)/4

expand

\frac{( x ^{3} + 6 ) ^{4}}{4}

\frac{x ^{12}}{4} + 6 x^{9} + 54 x^{6} + 216 x^{3} + 324

Solution steps

\frac{( x ^{3} + 6 ) ^{4}}{4}

(x^{3} + 6)^{4} = x^{12} + 24 x^{9} + 216 x^{6} + 864 x^{3} + 1296

= \frac{x ^{12} + 24 x ^{9} + 216 x ^{6} + 864 x ^{3} + 1296}{4}

Apply the fraction rule:

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

\frac{x ^{12} + 24 x ^{9} + 216 x ^{6} + 864 x ^{3} + 1296}{4} = \frac{x ^{12}}{4} + \frac{24 x ^{9}}{4} + \frac{216 x ^{6}}{4} + \frac{864 x ^{3}}{4} + \frac{1296}{4}

= \frac{x ^{12}}{4} + \frac{24 x ^{9}}{4} + \frac{216 x ^{6}}{4} + \frac{864 x ^{3}}{4} + \frac{1296}{4}

\frac{24 x ^{9}}{4} = 6 x^{9}

\frac{216 x ^{6}}{4} = 54 x^{6}

\frac{864 x ^{3}}{4} = 216 x^{3}

\frac{1296}{4} = 324

= \frac{x ^{12}}{4} + 6 x^{9} + 54 x^{6} + 216 x^{3} + 324

\frac{1}{( y - 1 ) y}

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

sin (t (t - \frac{π}{6}))

(x - 2) e^{3}

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

What is expand ((x^3+6)^4)/4 ?
The solution to expand ((x^3+6)^4)/4 is (x^{12})/4+6x^9+54x^6+216x^3+324