What is expand ((2x+1)^3)/6 ?

The solution to expand ((2x+1)^3)/6 is (4x^3)/3+2x^2+x+1/6

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expand ((2x+1)^3)/6

expand

\frac{( 2 x + 1 ) ^{3}}{6}

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

Solution steps

\frac{( 2 x + 1 ) ^{3}}{6}

(2 x + 1)^{3} = 8 x^{3} + 12 x^{2} + 6 x + 1

= \frac{8 x ^{3} + 12 x ^{2} + 6 x + 1}{6}

Apply the fraction rule:

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

\frac{8 x ^{3} + 12 x ^{2} + 6 x + 1}{6} = \frac{8 x ^{3}}{6} + \frac{12 x ^{2}}{6} + \frac{6 x}{6} + \frac{1}{6}

= \frac{8 x ^{3}}{6} + \frac{12 x ^{2}}{6} + \frac{6 x}{6} + \frac{1}{6}

Cancel

\frac{8 x ^{3}}{6} : \frac{4 x ^{3}}{3}

= \frac{4 x ^{3}}{3} + \frac{12 x ^{2}}{6} + \frac{6 x}{6} + \frac{1}{6}

Divide the numbers:

\frac{12}{6} = 2

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

Divide the numbers:

\frac{6}{6} = 1

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

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\frac{s ( s + 20 )}{11}

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What is expand ((2x+1)^3)/6 ?
The solution to expand ((2x+1)^3)/6 is (4x^3)/3+2x^2+x+1/6