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

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

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

expand

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

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

Solution steps

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

(x^{2} + 1)^{3} = x^{6} + 3 x^{4} + 3 x^{2} + 1

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{3}{3} = 1

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

2 (2 + 2)

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

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

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

(x^{2} + \frac{1}{x})^{10}

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