What is expand (2+x/2)^6 ?

The solution to expand (2+x/2)^6 is 64+96x+60x^2+20x^3+(15x^4)/4+(3x^5)/8+(x^6)/(64)

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expand (2+x/2)^6

expand

(2 + \frac{x}{2})^{6}

64 + 96 x + 60 x^{2} + 20 x^{3} + \frac{15 x ^{4}}{4} + \frac{3 x ^{5}}{8} + \frac{x ^{6}}{64}

Solution steps

(2 + \frac{x}{2})^{6}

Apply binomial theorem:

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

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

= i = 0 \sum 6 (i 6) \cdot 2^{(6 - i)} (\frac{x}{2})^{i}

Expand summation

= \frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 2^{6} (\frac{x}{2})^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 2^{5} (\frac{x}{2})^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 2^{4} (\frac{x}{2})^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 2^{3} (\frac{x}{2})^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 2^{2} (\frac{x}{2})^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 2^{1} (\frac{x}{2})^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 2^{0} (\frac{x}{2})^{6}

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 2^{6} (\frac{x}{2})^{0} : 64

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 2^{5} (\frac{x}{2})^{1} : 96 x

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 2^{4} (\frac{x}{2})^{2} : 60 x^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 2^{3} (\frac{x}{2})^{3} : 20 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 2^{2} (\frac{x}{2})^{4} : \frac{15 x ^{4}}{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 2^{1} (\frac{x}{2})^{5} : \frac{3 x ^{5}}{8}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 2^{0} (\frac{x}{2})^{6} : \frac{x ^{6}}{64}

= 64 + 96 x + 60 x^{2} + 20 x^{3} + \frac{15 x ^{4}}{4} + \frac{3 x ^{5}}{8} + \frac{x ^{6}}{64}

\frac{sin ( a ) - cot ( a ) ( 1 - cos ( a ) )}{1 - cos ( a )}

R (3, - 2, - 6) y S (5, 1, - 9)

(e^{x} + e^{- x} - 2)^{2}

\frac{1}{( x + i y ) ^{3} - 2 ( x + i y ) ^{2} + 2 ( x + i y )}

\frac{d}{d x} ((z) (9 x y z - e^{z}))

What is expand (2+x/2)^6 ?
The solution to expand (2+x/2)^6 is 64+96x+60x^2+20x^3+(15x^4)/4+(3x^5)/8+(x^6)/(64)