The given expression is
[tex](x-\frac{1}{x})^3[/tex]
According to Pascal's Triangle, the third row is 1 3 3 1.
This means the binomial expansions must have 4 terms, where each number belongs to each of them as a coefficient.
Now, the binomial expansion would be
[tex](x-\frac{1}{x})^3=x^3+3x^2(-\frac{1}{x})+3x(-\frac{1}{x})^2+(-\frac{1}{x})^3[/tex]
Now, we need to solve each parenthesis using the distributive property.
[tex]x^3-\frac{3x^2}{x}+\frac{3x}{x^2}-\frac{1}{x^3}[/tex]
Then, we simplify variables, remember that division of powers is solved by subtracting exponents
[tex]x^3-3x^{2-1}+3x^{1-2}-\frac{1}{x^3}=x^3-3x+3x^{-1}-\frac{1}{x^3}[/tex]
At last, we place the negative power as denominator
[tex]x^3-3x+\frac{3}{x}-\frac{1}{x^3}[/tex]
