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

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

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expand (x/2+1)^5

expand

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

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

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

x^{2} - 6 x + x y - 6 y

- 10 - 10

x^{2} x^{- 6}

\frac{12 2}{3}

- 460

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