Expand: x - (1 x )^3 - Vidyadip

Question

Expand: $x -\left(\frac{1}{x}\right)^3$

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Answer

$x-\left(\frac{1}{x}\right) 3=3 C_0(x) 3\left(\frac{1}{x}\right) 0-3 C_1(x) 2\left(\frac{1}{x}\right)+3 C_2(x) 1\left(\frac{1}{x}\right) 2-3 C_3(x) 0\left(\frac{1}{x}\right) 3$
$=x^3-\frac{3 x^2}{x}+\frac{3 x}{x^2}-\frac{1}{x^3}$
$=x^3-3 x+\frac{3}{x}-\frac{1}{x^3}$

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