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

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

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

expand

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

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

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

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

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

(5 cos (x) - cos (5 x)) (5 cos (x) - 5 cos (5 x))

(- \frac{5}{6}, - \frac{3}{2}) y (\frac{11}{2}, \frac{1}{3})

- 2 (x^{2} + 2Δ x^{2} + Δ^{2} x^{2}) + 1

(y - 3) (y + 23)

\frac{3 ( x ^{2} - x + 6 )}{4 ( x ^{2} - 9 )}

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