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

The solution to expand ((x^2-1)/(x^2))^3 is 1-3/(x^2)+3/(x^4)-1/(x^6)

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

expand

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

1 - \frac{3}{x ^{2}} + \frac{3}{x ^{4}} - \frac{1}{x ^{6}}

Solution steps

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

(x^{2})^{3} : x^{6}

= \frac{( x ^{2} - 1 ) ^{3}}{x ^{6}}

(x^{2} - 1)^{3} = x^{6} - 3 x^{4} + 3 x^{2} - 1

= \frac{x ^{6} - 3 x ^{4} + 3 x ^{2} - 1}{x ^{6}}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{6} - 3 x ^{4} + 3 x ^{2} - 1}{x ^{6}} = \frac{x ^{6}}{x ^{6}} - \frac{3 x ^{4}}{x ^{6}} + \frac{3 x ^{2}}{x ^{6}} - \frac{1}{x ^{6}}

= \frac{x ^{6}}{x ^{6}} - \frac{3 x ^{4}}{x ^{6}} + \frac{3 x ^{2}}{x ^{6}} - \frac{1}{x ^{6}}

Apply rule

\frac{a}{a} = 1

\frac{x ^{6}}{x ^{6}} = 1

= 1 - \frac{3 x ^{4}}{x ^{6}} + \frac{3 x ^{2}}{x ^{6}} - \frac{1}{x ^{6}}

Cancel

\frac{3 x ^{4}}{x ^{6}} : \frac{3}{x ^{2}}

= 1 - \frac{3}{x ^{2}} + \frac{3 x ^{2}}{x ^{6}} - \frac{1}{x ^{6}}

Cancel

\frac{3 x ^{2}}{x ^{6}} : \frac{3}{x ^{4}}

= 1 - \frac{3}{x ^{2}} + \frac{3}{x ^{4}} - \frac{1}{x ^{6}}

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What is expand ((x^2-1)/(x^2))^3 ?
The solution to expand ((x^2-1)/(x^2))^3 is 1-3/(x^2)+3/(x^4)-1/(x^6)