What is expand (x-1/x)^4 ?

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

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expand (x-1/x)^4

expand

(x - \frac{1}{x})^{4}

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

Solution steps

(x - \frac{1}{x})^{4}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = x, b = - \frac{1}{x}

= i = 0 \sum 4 (i 4) x^{(4 - i)} (- \frac{1}{x})^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} (- \frac{1}{x})^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (- \frac{1}{x})^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (- \frac{1}{x})^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (- \frac{1}{x})^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (- \frac{1}{x})^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} (- \frac{1}{x})^{0} : x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (- \frac{1}{x})^{1} : - 4 x^{2}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (- \frac{1}{x})^{2} : 6

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (- \frac{1}{x})^{3} : - \frac{4}{x ^{2}}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (- \frac{1}{x})^{4} : \frac{1}{x ^{4}}

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

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