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

The solution to expand (1+4/(x^2))^4 is 1+(16)/(x^2)+(96)/(x^4)+(256)/(x^6)+(256)/(x^8)

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expand (1+4/(x^2))^4

expand

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

1 + \frac{16}{x ^{2}} + \frac{96}{x ^{4}} + \frac{256}{x ^{6}} + \frac{256}{x ^{8}}

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 1^{1} (\frac{4}{x ^{2}})^{3} : \frac{256}{x ^{6}}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} (\frac{4}{x ^{2}})^{4} : \frac{256}{x ^{8}}

= 1 + \frac{16}{x ^{2}} + \frac{96}{x ^{4}} + \frac{256}{x ^{6}} + \frac{256}{x ^{8}}

(cos (x) - 1)^{2}

(x - y) (x + y)

(9 + 2 x sin (y)) d x - x^{2} cos (y) d y

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

(sec (a) + tan (a)) (1 - sin (a))

What is expand (1+4/(x^2))^4 ?
The solution to expand (1+4/(x^2))^4 is 1+(16)/(x^2)+(96)/(x^4)+(256)/(x^6)+(256)/(x^8)