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

The solution to expand (x^3-1/(x^2))^3 is (x^{15}-3x^{10}+3x^5-1)/(x^6)

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

expand

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

\frac{x ^{15} - 3 x ^{10} + 3 x ^{5} - 1}{x ^{6}}

Solution steps

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

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

Simplify

(x^{3})^{3} - 3 (x^{3})^{2} \frac{1}{x ^{2}} + 3 x^{3} (\frac{1}{x ^{2}})^{2} - (\frac{1}{x ^{2}})^{3} : \frac{x ^{15} - 3 x ^{10} + 3 x ^{5} - 1}{x ^{6}}

= \frac{x ^{15} - 3 x ^{10} + 3 x ^{5} - 1}{x ^{6}}

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

, (2 t^{2} - 1) 2 d t

(- 3 - 5 i)^{6}

\frac{x ^{5} + 2 x ^{3} - 2 x ^{2} - 2 x - 24}{( x - 1 ) ^{2} ( x ^{2} + 4 ) ^{2}}

What is expand (x^3-1/(x^2))^3 ?
The solution to expand (x^3-1/(x^2))^3 is (x^{15}-3x^{10}+3x^5-1)/(x^6)