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

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

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

expand

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

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

Solution steps

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

(2 + x^{2})^{3} = 8 + 12 x^{2} + 6 x^{4} + x^{6}

= \frac{8 + 12 x ^{2} + 6 x ^{4} + x ^{6}}{6}

Apply the fraction rule:

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

\frac{8 + 12 x ^{2} + 6 x ^{4} + x ^{6}}{6} = \frac{8}{6} + \frac{12 x ^{2}}{6} + \frac{6 x ^{4}}{6} + \frac{x ^{6}}{6}

= \frac{8}{6} + \frac{12 x ^{2}}{6} + \frac{6 x ^{4}}{6} + \frac{x ^{6}}{6}

Cancel

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

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

Divide the numbers:

\frac{12}{6} = 2

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

Divide the numbers:

\frac{6}{6} = 1

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

Rewrite in standard form

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

x - 1 \cdot (x - 2)

(x^{(8)} - 4 x^{(3)} - x) d x

(sec (x) - 1) (sec (x))

\frac{( 2 y + 8 ) ^{2}}{4}

e^{(x^{2} - 3 x)^{2}}

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