What is expand ((3x-2)^4)/4 ?

The solution to expand ((3x-2)^4)/4 is (81x^4)/4-54x^3+54x^2-24x+4

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expand ((3x-2)^4)/4

expand

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

\frac{81 x ^{4}}{4} - 54 x^{3} + 54 x^{2} - 24 x + 4

Solution steps

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

(3 x - 2)^{4} = 81 x^{4} - 216 x^{3} + 216 x^{2} - 96 x + 16

= \frac{81 x ^{4} - 216 x ^{3} + 216 x ^{2} - 96 x + 16}{4}

Apply the fraction rule:

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

\frac{81 x ^{4} - 216 x ^{3} + 216 x ^{2} - 96 x + 16}{4} = \frac{81 x ^{4}}{4} - \frac{216 x ^{3}}{4} + \frac{216 x ^{2}}{4} - \frac{96 x}{4} + \frac{16}{4}

= \frac{81 x ^{4}}{4} - \frac{216 x ^{3}}{4} + \frac{216 x ^{2}}{4} - \frac{96 x}{4} + \frac{16}{4}

\frac{216 x ^{3}}{4} = 54 x^{3}

\frac{216 x ^{2}}{4} = 54 x^{2}

\frac{96 x}{4} = 24 x

\frac{16}{4} = 4

= \frac{81 x ^{4}}{4} - 54 x^{3} + 54 x^{2} - 24 x + 4

(1 - cos (x))^{4}

\frac{10 x ^{2} y ^{2} - 8 x y ^{3} + 6 y}{2 y ^{2}}

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

sin^{2} (x) (cot (x) + 1)^{2}

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

What is expand ((3x-2)^4)/4 ?
The solution to expand ((3x-2)^4)/4 is (81x^4)/4-54x^3+54x^2-24x+4