What is expand ((4+x)^3)/8 ?

The solution to expand ((4+x)^3)/8 is (x^3)/8+(3x^2)/2+6x+8

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expand ((4+x)^3)/8

expand

\frac{( 4 + x ) ^{3}}{8}

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

Solution steps

\frac{( 4 + x ) ^{3}}{8}

(4 + x)^{3} = 64 + 48 x + 12 x^{2} + x^{3}

= \frac{64 + 48 x + 12 x ^{2} + x ^{3}}{8}

Apply the fraction rule:

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

\frac{64 + 48 x + 12 x ^{2} + x ^{3}}{8} = \frac{64}{8} + \frac{48 x}{8} + \frac{12 x ^{2}}{8} + \frac{x ^{3}}{8}

= \frac{64}{8} + \frac{48 x}{8} + \frac{12 x ^{2}}{8} + \frac{x ^{3}}{8}

Divide the numbers:

\frac{64}{8} = 8

= 8 + \frac{48 x}{8} + \frac{12 x ^{2}}{8} + \frac{x ^{3}}{8}

Divide the numbers:

\frac{48}{8} = 6

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

Cancel

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

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

Rewrite in standard form

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

3 (e^{3 t} + C e^{- t}) + 8 e^{- t}

1 + (3 x^{2} - 6 x)^{2}

\frac{1}{( 2 + 5 x ) ^{3}}

\frac{( 2 x a + b ) ^{2}}{4 a ^{2}}

(4 - x) e - 2

What is expand ((4+x)^3)/8 ?
The solution to expand ((4+x)^3)/8 is (x^3)/8+(3x^2)/2+6x+8