What is expand (3+x/2)^5 ?

The solution to expand (3+x/2)^5 is 243+(405x)/2+(135x^2)/2+(45x^3)/4+(15x^4)/(16)+(x^5)/(32)

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expand (3+x/2)^5

expand

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

243 + \frac{405 x}{2} + \frac{135 x ^{2}}{2} + \frac{45 x ^{3}}{4} + \frac{15 x ^{4}}{16} + \frac{x ^{5}}{32}

Solution steps

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

Apply binomial theorem:

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

a = 3, b = \frac{x}{2}

= i = 0 \sum 5 (i 5) \cdot 3^{(5 - i)} (\frac{x}{2})^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 3^{5} (\frac{x}{2})^{0} : 243

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 3^{4} (\frac{x}{2})^{1} : \frac{405 x}{2}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 3^{3} (\frac{x}{2})^{2} : \frac{135 x ^{2}}{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 3^{2} (\frac{x}{2})^{3} : \frac{45 x ^{3}}{4}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 3^{1} (\frac{x}{2})^{4} : \frac{15 x ^{4}}{16}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 3^{0} (\frac{x}{2})^{5} : \frac{x ^{5}}{32}

= 243 + \frac{405 x}{2} + \frac{135 x ^{2}}{2} + \frac{45 x ^{3}}{4} + \frac{15 x ^{4}}{16} + \frac{x ^{5}}{32}

- x + h - 3 (3 x^{2} - 2 x)

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

\frac{d ^{2}}{d x ^{2}} ((y^{2}) (- 3 x^{3} y^{2} - x^{2} y - 3 x - 2 y^{2}))

cos (t - 1) U (t - 1)

(a^{2} - \frac{1}{4})^{4}

What is expand (3+x/2)^5 ?
The solution to expand (3+x/2)^5 is 243+(405x)/2+(135x^2)/2+(45x^3)/4+(15x^4)/(16)+(x^5)/(32)