What is expand (n-1/n)^3 ?

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

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expand (n-1/n)^3

expand

(n - \frac{1}{n})^{3}

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

Solution steps

(n - \frac{1}{n})^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

n^{3} - 3 n^{2} \frac{1}{n} + 3 n (\frac{1}{n})^{2} - (\frac{1}{n})^{3} : \frac{n ^{6} - 3 n ^{4} + 3 n ^{2} - 1}{n ^{3}}

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

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

\frac{( - 1 ) ^{k} k !}{3 ^{k} ( k + 1 )}

\frac{s - 10}{( s + 4 ) ( s ^{2} + 1 )}

(ey + 1)^{2}

(e + 1)^{3}

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