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

The solution to expand (x+1/2)^5 is x^5+(5x^4)/2+(5x^3)/2+(5x^2)/4+(5x)/(16)+1/32

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expand (x+1/2)^5

expand

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

x^{5} + \frac{5 x ^{4}}{2} + \frac{5 x ^{3}}{2} + \frac{5 x ^{2}}{4} + \frac{5 x}{16} + \frac{1}{32}

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} (\frac{1}{2})^{4} : \frac{5 x}{16}

Simplify

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

= x^{5} + \frac{5 x ^{4}}{2} + \frac{5 x ^{3}}{2} + \frac{5 x ^{2}}{4} + \frac{5 x}{16} + \frac{1}{32}

(x - 8) + 8 + 2

\frac{3 - 7 i}{2 i}

9 - 218

- 4 (- 8 w - 4 x) - 7 x - 10 (- 10 x + 8 w)

6 y - 18

What is expand (x+1/2)^5 ?
The solution to expand (x+1/2)^5 is x^5+(5x^4)/2+(5x^3)/2+(5x^2)/4+(5x)/(16)+1/32