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}}

(5 x - 10) (3 - x)

\frac{20 ( s + 1 )}{s ( 5 s ^{2} + 6 s + 2 )}

(- x^{2} + 0.5 x + 5) d x

(a + 5) - \frac{b}{b - 4} + \frac{2 ( b + 3 )}{a}

(\frac{a}{6} + \frac{b ^{3}}{5}) (\frac{a}{6} - \frac{b ^{3}}{5})

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)