What is expand (x-1/x)^8 ?

The solution to expand (x-1/x)^8 is x^8-8x^6+28x^4-56x^2+70-(56)/(x^2)+(28)/(x^4)-8/(x^6)+1/(x^8)

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expand (x-1/x)^8

expand

(x - \frac{1}{x})^{8}

x^{8} - 8 x^{6} + 28 x^{4} - 56 x^{2} + 70 - \frac{56}{x ^{2}} + \frac{28}{x ^{4}} - \frac{8}{x ^{6}} + \frac{1}{x ^{8}}

Solution steps

(x - \frac{1}{x})^{8}

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 8 (i 8) x^{(8 - i)} (- \frac{1}{x})^{i}

Expand summation

= \frac{8 !}{0 ! ( 8 - 0 ) !} x^{8} (- \frac{1}{x})^{0} + \frac{8 !}{1 ! ( 8 - 1 ) !} x^{7} (- \frac{1}{x})^{1} + \frac{8 !}{2 ! ( 8 - 2 ) !} x^{6} (- \frac{1}{x})^{2} + \frac{8 !}{3 ! ( 8 - 3 ) !} x^{5} (- \frac{1}{x})^{3} + \frac{8 !}{4 ! ( 8 - 4 ) !} x^{4} (- \frac{1}{x})^{4} + \frac{8 !}{5 ! ( 8 - 5 ) !} x^{3} (- \frac{1}{x})^{5} + \frac{8 !}{6 ! ( 8 - 6 ) !} x^{2} (- \frac{1}{x})^{6} + \frac{8 !}{7 ! ( 8 - 7 ) !} x^{1} (- \frac{1}{x})^{7} + \frac{8 !}{8 ! ( 8 - 8 ) !} x^{0} (- \frac{1}{x})^{8}

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} x^{8} (- \frac{1}{x})^{0} : x^{8}

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} x^{7} (- \frac{1}{x})^{1} : - 8 x^{6}

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} x^{6} (- \frac{1}{x})^{2} : 28 x^{4}

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} x^{5} (- \frac{1}{x})^{3} : - 56 x^{2}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} x^{4} (- \frac{1}{x})^{4} : 70

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} x^{3} (- \frac{1}{x})^{5} : - \frac{56}{x ^{2}}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} x^{2} (- \frac{1}{x})^{6} : \frac{28}{x ^{4}}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} x^{1} (- \frac{1}{x})^{7} : - \frac{8}{x ^{6}}

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} x^{0} (- \frac{1}{x})^{8} : \frac{1}{x ^{8}}

= x^{8} - 8 x^{6} + 28 x^{4} - 56 x^{2} + 70 - \frac{56}{x ^{2}} + \frac{28}{x ^{4}} - \frac{8}{x ^{6}} + \frac{1}{x ^{8}}

(- 1 + i)^{7}

\frac{1}{( s ^{2} + 1 ) ^{2}}

(3 - x)^{2}

(3 x - \frac{2}{3})^{7}

(1 + \frac{4}{x ^{2}})^{4}

What is expand (x-1/x)^8 ?
The solution to expand (x-1/x)^8 is x^8-8x^6+28x^4-56x^2+70-(56)/(x^2)+(28)/(x^4)-8/(x^6)+1/(x^8)