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

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

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

expand

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

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

Solution steps

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

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{6}{6} = 1

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

Divide the numbers:

\frac{12}{6} = 2

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

Cancel

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

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

δ (x) \cdot (x - 1)

x - \frac{( x ^{2} - 2 ) ln ( x )}{2 x ^{2} ln ( x ) + x ^{2} - 2}

\frac{2}{( s + 1 ) ^{2}}

\frac{6}{( 1 + 5.1 s ) ( 1 + 0.1 s )}

x 2 + 4 x

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