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

The solution to expand (2+3/(x^2))^4 is 16+(96)/(x^2)+(216)/(x^4)+(216)/(x^6)+(81)/(x^8)

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

expand

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

16 + \frac{96}{x ^{2}} + \frac{216}{x ^{4}} + \frac{216}{x ^{6}} + \frac{81}{x ^{8}}

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 2^{4} (\frac{3}{x ^{2}})^{0} : 16

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 2^{3} (\frac{3}{x ^{2}})^{1} : \frac{96}{x ^{2}}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 2^{2} (\frac{3}{x ^{2}})^{2} : \frac{216}{x ^{4}}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 2^{1} (\frac{3}{x ^{2}})^{3} : \frac{216}{x ^{6}}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 2^{0} (\frac{3}{x ^{2}})^{4} : \frac{81}{x ^{8}}

= 16 + \frac{96}{x ^{2}} + \frac{216}{x ^{4}} + \frac{216}{x ^{6}} + \frac{81}{x ^{8}}

(2 - x) (2 + x)

\frac{sec ^{2} ( x ) - tan ( x ) ( tan ( x ) - 1 )}{sec ( x )}

cos (x) sin (x) (sec (x) + cot (x))

\frac{x + 5}{( x - 1 ) ( x + 2 )}

lo g_{10} (x) (x + 1)^{4}

What is expand (2+3/(x^2))^4 ?
The solution to expand (2+3/(x^2))^4 is 16+(96)/(x^2)+(216)/(x^4)+(216)/(x^6)+(81)/(x^8)