What is expand (x-2/x)^4 ?

The solution to expand (x-2/x)^4 is x^4-8x^2+24-(32)/(x^2)+(16)/(x^4)

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expand (x-2/x)^4

expand

(x - \frac{2}{x})^{4}

x^{4} - 8 x^{2} + 24 - \frac{32}{x ^{2}} + \frac{16}{x ^{4}}

Solution steps

(x - \frac{2}{x})^{4}

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (- \frac{2}{x})^{1} : - 8 x^{2}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (- \frac{2}{x})^{2} : 24

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (- \frac{2}{x})^{3} : - \frac{32}{x ^{2}}

Simplify

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

= x^{4} - 8 x^{2} + 24 - \frac{32}{x ^{2}} + \frac{16}{x ^{4}}

\frac{1}{( 7 + x ) ^{2}}

(a - \frac{1}{9}) (a + \frac{1}{9})

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

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

\frac{1}{( x - 1 ) ^{3}}

What is expand (x-2/x)^4 ?
The solution to expand (x-2/x)^4 is x^4-8x^2+24-(32)/(x^2)+(16)/(x^4)