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

The solution to expand (x^2+1/x)^3 is (x^9+3x^6+3x^3+1)/(x^3)

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

expand

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

\frac{x ^{9} + 3 x ^{6} + 3 x ^{3} + 1}{x ^{3}}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(x^{2})^{3} + 3 (x^{2})^{2} \frac{1}{x} + 3 x^{2} (\frac{1}{x})^{2} + (\frac{1}{x})^{3} : \frac{x ^{9} + 3 x ^{6} + 3 x ^{3} + 1}{x ^{3}}

= \frac{x ^{9} + 3 x ^{6} + 3 x ^{3} + 1}{x ^{3}}

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

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

8 cos^{2} (2 t) + (t - 5)^{2} - 7 e^{4 t}

δ (x - 3)

\frac{- x ^{2} - 9}{( x ^{2} - 9 ) ^{2}}

What is expand (x^2+1/x)^3 ?
The solution to expand (x^2+1/x)^3 is (x^9+3x^6+3x^3+1)/(x^3)