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

The solution to expand ((4+x^2)^3)/6 is (x^6)/6+2x^4+8x^2+32/3

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expand ((4+x^2)^3)/6

expand

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

\frac{x ^{6}}{6} + 2 x^{4} + 8 x^{2} + \frac{32}{3}

Solution steps

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

(4 + x^{2})^{3} = 64 + 48 x^{2} + 12 x^{4} + x^{6}

= \frac{64 + 48 x ^{2} + 12 x ^{4} + x ^{6}}{6}

Apply the fraction rule:

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

\frac{64 + 48 x ^{2} + 12 x ^{4} + x ^{6}}{6} = \frac{64}{6} + \frac{48 x ^{2}}{6} + \frac{12 x ^{4}}{6} + \frac{x ^{6}}{6}

= \frac{64}{6} + \frac{48 x ^{2}}{6} + \frac{12 x ^{4}}{6} + \frac{x ^{6}}{6}

Cancel

\frac{64}{6} : \frac{32}{3}

= \frac{32}{3} + \frac{48 x ^{2}}{6} + \frac{12 x ^{4}}{6} + \frac{x ^{6}}{6}

Divide the numbers:

\frac{48}{6} = 8

= \frac{32}{3} + 8 x^{2} + \frac{12 x ^{4}}{6} + \frac{x ^{6}}{6}

Divide the numbers:

\frac{12}{6} = 2

= \frac{32}{3} + 8 x^{2} + 2 x^{4} + \frac{x ^{6}}{6}

Rewrite in standard form

= \frac{x ^{6}}{6} + 2 x^{4} + 8 x^{2} + \frac{32}{3}

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

\frac{( x - 2 ) ( x - 3 )}{12}

(- 2, 4) y (3, - 3)

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

\frac{( 8 x - 3 ) ^{2}}{64}

What is expand ((4+x^2)^3)/6 ?
The solution to expand ((4+x^2)^3)/6 is (x^6)/6+2x^4+8x^2+32/3