What is expand (x^2+3/x)^4 ?

The solution to expand (x^2+3/x)^4 is x^8+12x^5+54x^2+(108)/x+(81)/(x^4)

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expand (x^2+3/x)^4

expand

(x^{2} + \frac{3}{x})^{4}

x^{8} + 12 x^{5} + 54 x^{2} + \frac{108}{x} + \frac{81}{x ^{4}}

Solution steps

(x^{2} + \frac{3}{x})^{4}

Apply binomial theorem:

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

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

= i = 0 \sum 4 (i 4) (x^{2})^{(4 - i)} (\frac{3}{x})^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (x^{2})^{4} (\frac{3}{x})^{0} : x^{8}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (x^{2})^{3} (\frac{3}{x})^{1} : 12 x^{5}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (x^{2})^{2} (\frac{3}{x})^{2} : 54 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (x^{2})^{1} (\frac{3}{x})^{3} : \frac{108}{x}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (x^{2})^{0} (\frac{3}{x})^{4} : \frac{81}{x ^{4}}

= x^{8} + 12 x^{5} + 54 x^{2} + \frac{108}{x} + \frac{81}{x ^{4}}

b (5, - \frac{π}{3})

(2 t - 3) e^{(\frac{( t + 2 )}{3})}

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

(a + b) l e f t (a - b)

(2 π + 16) \times 12

What is expand (x^2+3/x)^4 ?
The solution to expand (x^2+3/x)^4 is x^8+12x^5+54x^2+(108)/x+(81)/(x^4)