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

The solution to expand (1/x i-1)^3 is (3-x^2)/(x^2)+(-1+3x^2)/(x^3)i

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expand (1/x i-1)^3

expand

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

\frac{3 - x ^{2}}{x ^{2}} + \frac{- 1 + 3 x ^{2}}{x ^{3}} i

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(\frac{1}{x} i)^{3} - 3 (\frac{1}{x} i)^{2} \cdot 1 + 3 \cdot \frac{1}{x} i 1^{2} - 1^{3} : - \frac{i}{x ^{3}} + 3 \cdot \frac{1}{x ^{2}} + 3 \cdot \frac{1}{x} i - 1

= - \frac{i}{x ^{3}} + 3 \cdot \frac{1}{x ^{2}} + 3 \cdot \frac{1}{x} i - 1

Simplify

- \frac{i}{x ^{3}} + 3 \cdot \frac{1}{x ^{2}} + 3 \cdot \frac{1}{x} i - 1 : \frac{3 - x ^{2}}{x ^{2}} + \frac{- 1 + 3 x ^{2}}{x ^{3}} i

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

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