What is expand (4+1/2 x)^6 ?

The solution to expand (4+1/2 x)^6 is 4096+3072x+960x^2+160x^3+15x^4+(3x^5)/4+(x^6)/(64)

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expand (4+1/2 x)^6

expand

(4 + \frac{1}{2} x)^{6}

4096 + 3072 x + 960 x^{2} + 160 x^{3} + 15 x^{4} + \frac{3 x ^{5}}{4} + \frac{x ^{6}}{64}

Solution steps

(4 + \frac{1}{2} x)^{6}

Apply binomial theorem:

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

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

= i = 0 \sum 6 (i 6) \cdot 4^{(6 - i)} (\frac{1}{2} x)^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 4^{6} (\frac{1}{2} x)^{0} : 4096

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 4^{5} (\frac{1}{2} x)^{1} : 3072 x

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 4^{4} (\frac{1}{2} x)^{2} : 960 x^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 4^{3} (\frac{1}{2} x)^{3} : 160 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 4^{2} (\frac{1}{2} x)^{4} : 15 x^{4}

Simplify

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

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 4^{0} (\frac{1}{2} x)^{6} : \frac{x ^{6}}{64}

= 4096 + 3072 x + 960 x^{2} + 160 x^{3} + 15 x^{4} + \frac{3 x ^{5}}{4} + \frac{x ^{6}}{64}

\frac{- 7 s ^{2} - 440}{( s ^{2} + 64 ) ( s + a )}

(5 t^{2} + t - t^{3}) \cdot (sin (t) - cos (t))

- \frac{2}{s ^{2} ( s ^{2} + 1 )}

(1 + cos^{2} (7 x))^{3}

\frac{- 6 s ^{2} + 12 s - 117}{( s - 2 ) ( - s ^{3} - 9 s )}

What is expand (4+1/2 x)^6 ?
The solution to expand (4+1/2 x)^6 is 4096+3072x+960x^2+160x^3+15x^4+(3x^5)/4+(x^6)/(64)