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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (x-1/x)^5

expand

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

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

Solution steps

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

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

(y ln (y) - e^{- x y}) d x + (\frac{1}{y} + x ln (y)) d y

\frac{( n + 1 ) ( x + 2 )}{3 n}

2 e^{35} \cdot \frac{d}{d s} (\frac{1}{e ^{35} ( s + 5 )})

e^{t} (- t e^{- t} - e^{- t} + 1)

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

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