What is expand (5+x/2)^4 ?

The solution to expand (5+x/2)^4 is 625+250x+(75x^2)/2+(5x^3)/2+(x^4)/(16)

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expand (5+x/2)^4

expand

(5 + \frac{x}{2})^{4}

625 + 250 x + \frac{75 x ^{2}}{2} + \frac{5 x ^{3}}{2} + \frac{x ^{4}}{16}

Solution steps

(5 + \frac{x}{2})^{4}

Apply binomial theorem:

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

a = 5, b = \frac{x}{2}

= i = 0 \sum 4 (i 4) \cdot 5^{(4 - i)} (\frac{x}{2})^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 5^{4} (\frac{x}{2})^{0} : 625

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 5^{3} (\frac{x}{2})^{1} : 250 x

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 5^{2} (\frac{x}{2})^{2} : \frac{75 x ^{2}}{2}

Simplify

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

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 5^{0} (\frac{x}{2})^{4} : \frac{x ^{4}}{16}

= 625 + 250 x + \frac{75 x ^{2}}{2} + \frac{5 x ^{3}}{2} + \frac{x ^{4}}{16}

\frac{d}{d y} ((z (y, x)) (x y^{5} - x^{2} y))

3 (3 sin^{2} (x) - 4 cos^{2} (x))

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

\frac{d ^{2}}{d x ^{2}} ((y) (x^{4} + y^{4} - 16))

(10 - 6 y) + (x + 3) i

What is expand (5+x/2)^4 ?
The solution to expand (5+x/2)^4 is 625+250x+(75x^2)/2+(5x^3)/2+(x^4)/(16)