Using binomial theorem, expand each of the following: (1 + x/2 - 2/x)^4,x≠0

Question

Using binomial theorem, expand each of the following: \(\Big(1+\frac{x}{2} -\frac{2}{x}\Big)^4\), x≠0

Answer 1

 To find: Expansion of \(\Big(1+\frac{x}{2} -\frac{2}{x}\Big)^4\), x≠0

Formula used: (i)

ⁿC_r = \(\frac{n!}{(n-r)!(r)!}\) 

(Substituting value of b from eqn. (i)

We need the value of a⁴ ,a³ and a² , where a = \((1+\frac{x}{2})\)

For ,  \((1+\frac{x}{2})\) Applying Binomial theorem