What is expand (x-2/x)^5 ?

The solution to expand (x-2/x)^5 is x^5-10x^3+40x-(80)/x+(80)/(x^3)-(32)/(x^5)

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expand (x-2/x)^5

expand

(x - \frac{2}{x})^{5}

x^{5} - 10 x^{3} + 40 x - \frac{80}{x} + \frac{80}{x ^{3}} - \frac{32}{x ^{5}}

Solution steps

(x - \frac{2}{x})^{5}

Apply binomial theorem:

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

a = x, b = - \frac{2}{x}

= i = 0 \sum 5 (i 5) x^{(5 - i)} (- \frac{2}{x})^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} x^{5} (- \frac{2}{x})^{0} : x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} x^{4} (- \frac{2}{x})^{1} : - 10 x^{3}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} (- \frac{2}{x})^{2} : 40 x

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} (- \frac{2}{x})^{3} : - \frac{80}{x}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} (- \frac{2}{x})^{4} : \frac{80}{x ^{3}}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} x^{0} (- \frac{2}{x})^{5} : - \frac{32}{x ^{5}}

= x^{5} - 10 x^{3} + 40 x - \frac{80}{x} + \frac{80}{x ^{3}} - \frac{32}{x ^{5}}

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

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

(x + 37) (x - 7)

\frac{1}{( 1 - i 3 ) ^{4}}

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

What is expand (x-2/x)^5 ?
The solution to expand (x-2/x)^5 is x^5-10x^3+40x-(80)/x+(80)/(x^3)-(32)/(x^5)