What is expand (2x-1/x)^5 ?

The solution to expand (2x-1/x)^5 is 32x^5-80x^3+80x-(40)/x+(10)/(x^3)-1/(x^5)

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expand (2x-1/x)^5

expand

(2 x - \frac{1}{x})^{5}

32 x^{5} - 80 x^{3} + 80 x - \frac{40}{x} + \frac{10}{x ^{3}} - \frac{1}{x ^{5}}

Solution steps

(2 x - \frac{1}{x})^{5}

Apply binomial theorem:

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

a = 2 x, b = - \frac{1}{x}

= i = 0 \sum 5 (i 5) (2 x)^{(5 - i)} (- \frac{1}{x})^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (2 x)^{5} (- \frac{1}{x})^{0} : 32 x^{5}

Simplify

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

Simplify

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

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (2 x)^{2} (- \frac{1}{x})^{3} : - \frac{40}{x}

Simplify

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

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (2 x)^{0} (- \frac{1}{x})^{5} : - \frac{1}{x ^{5}}

= 32 x^{5} - 80 x^{3} + 80 x - \frac{40}{x} + \frac{10}{x ^{3}} - \frac{1}{x ^{5}}

(cos (θ) - 1) (sin (θ) - 1)

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

(- sin (t) e^{t} + cos (t) e^{t})^{2}

(3 x + 5) (x - 25)

(1 - x^{2}) (1 - x^{2})

What is expand (2x-1/x)^5 ?
The solution to expand (2x-1/x)^5 is 32x^5-80x^3+80x-(40)/x+(10)/(x^3)-1/(x^5)