What is expand ((2x+c)^3)/8 ?

The solution to expand ((2x+c)^3)/8 is x^3+(3cx^2)/2+(3c^2x)/4+(c^3)/8

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expand ((2x+c)^3)/8

expand

\frac{( 2 x + c ) ^{3}}{8}

x^{3} + \frac{3 c x ^{2}}{2} + \frac{3 c ^{2} x}{4} + \frac{c ^{3}}{8}

Solution steps

\frac{( 2 x + c ) ^{3}}{8}

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{8}{8} = 1

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

Cancel

\frac{12 c x ^{2}}{8} : \frac{3 c x ^{2}}{2}

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

Cancel

\frac{6 c ^{2} x}{8} : \frac{3 c ^{2} x}{4}

= x^{3} + \frac{3 c x ^{2}}{2} + \frac{3 c ^{2} x}{4} + \frac{c ^{3}}{8}

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\frac{5}{3} + \frac{7}{4}

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What is expand ((2x+c)^3)/8 ?
The solution to expand ((2x+c)^3)/8 is x^3+(3cx^2)/2+(3c^2x)/4+(c^3)/8