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

The solution to expand (x+2/x)^3 is (x^6+6x^4+12x^2+8)/(x^3)

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expand (x+2/x)^3

expand

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

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

Solution steps

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

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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

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

Simplify

x^{3} + 3 x^{2} \frac{2}{x} + 3 x (\frac{2}{x})^{2} + (\frac{2}{x})^{3} : \frac{x ^{6} + 6 x ^{4} + 12 x ^{2} + 8}{x ^{3}}

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

x^{\frac{4}{5}} (x + 3)

\frac{1}{x ^{3}} y^{3} (0 = x d y + (y^{3} x + y) d x)

\frac{( sec ^{2} ( \frac{x}{2} ) )}{( tan ( \frac{x}{2} ) + 1 ) ^{2}}

(1 + x^{4}) (x^{2} - \frac{1}{3})

\frac{6 y - 8 x}{5 ( x ^{2} + 4 y ^{2} )}

What is expand (x+2/x)^3 ?
The solution to expand (x+2/x)^3 is (x^6+6x^4+12x^2+8)/(x^3)