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

The solution to expand ((1+sqrt(x))^3)/3 is 1/3+sqrt(x)+x+(x^{3/2})/3

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expand ((1+sqrt(x))^3)/3

expand

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

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

Solution steps

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

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{3}{3} = 1

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

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\frac{x + 1 - 2}{x ( x - 3 )}

What is expand ((1+sqrt(x))^3)/3 ?
The solution to expand ((1+sqrt(x))^3)/3 is 1/3+sqrt(x)+x+(x^{3/2})/3