What is expand (2-1/(4x))^5 ?

The solution to expand (2-1/(4x))^5 is 32-(20)/x+5/(x^2)-5/(8x^3)+5/(128x^4)-1/(1024x^5)

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expand (2-1/(4x))^5

expand

(2 - \frac{1}{4 x})^{5}

32 - \frac{20}{x} + \frac{5}{x ^{2}} - \frac{5}{8 x ^{3}} + \frac{5}{128 x ^{4}} - \frac{1}{1024 x ^{5}}

Solution steps

(2 - \frac{1}{4 x})^{5}

Apply binomial theorem:

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

a = 2, b = - \frac{1}{4 x}

= i = 0 \sum 5 (i 5) \cdot 2^{(5 - i)} (- \frac{1}{4 x})^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 2^{5} (- \frac{1}{4 x})^{0} : 32

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 2^{4} (- \frac{1}{4 x})^{1} : - \frac{20}{x}

Simplify

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

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 2^{2} (- \frac{1}{4 x})^{3} : - \frac{5}{8 x ^{3}}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 2^{1} (- \frac{1}{4 x})^{4} : \frac{5}{128 x ^{4}}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 2^{0} (- \frac{1}{4 x})^{5} : - \frac{1}{1024 x ^{5}}

= 32 - \frac{20}{x} + \frac{5}{x ^{2}} - \frac{5}{8 x ^{3}} + \frac{5}{128 x ^{4}} - \frac{1}{1024 x ^{5}}

1 + \frac{k}{m s ^{2}} (\frac{s + a}{s + b})

2 (1 + sin (x))

7 sin (22 (x - 13)) - 21

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

(a cos (x) + b sin (x)) (a sin (x) + b cos (x))

What is expand (2-1/(4x))^5 ?
The solution to expand (2-1/(4x))^5 is 32-(20)/x+5/(x^2)-5/(8x^3)+5/(128x^4)-1/(1024x^5)