What is expand (2x+1/x)^4 ?

The solution to expand (2x+1/x)^4 is 16x^4+32x^2+24+8/(x^2)+1/(x^4)

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expand (2x+1/x)^4

expand

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

16 x^{4} + 32 x^{2} + 24 + \frac{8}{x ^{2}} + \frac{1}{x ^{4}}

Solution steps

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

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 4 (i 4) (2 x)^{(4 - i)} (\frac{1}{x})^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (2 x)^{4} (\frac{1}{x})^{0} : 16 x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (2 x)^{3} (\frac{1}{x})^{1} : 32 x^{2}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (2 x)^{2} (\frac{1}{x})^{2} : 24

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (2 x)^{1} (\frac{1}{x})^{3} : \frac{8}{x ^{2}}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (2 x)^{0} (\frac{1}{x})^{4} : \frac{1}{x ^{4}}

= 16 x^{4} + 32 x^{2} + 24 + \frac{8}{x ^{2}} + \frac{1}{x ^{4}}

(a, b) (b, - a)

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

(x + y^{'} (x)) (x + y)

\frac{d}{d x} ((e^{- 0.5 x}) (4 - x)) - 2

(x + y i)^{5}

What is expand (2x+1/x)^4 ?
The solution to expand (2x+1/x)^4 is 16x^4+32x^2+24+8/(x^2)+1/(x^4)