Question

Find the coefficient of `x` in the expansion of `(1+x^2)(x/2-4/x)^6`. Can Anyone pls solve step by step with binomial formula?

Answer 1

`0`

Explanation:

Given:

`(1+x^2)(x/2-4/x)^6`

At first sight it might look like you will get a mixture of even and odd degree terms when this is multiplied out, but looking a little closer it becomes clear that this is not so.

In particular, note that:

`(1+x^2)(x/2-4/x)^6 = 1/x^6(1+x^2)(x^2/2-4)^6`

The right hand side only contains terms of even degree.

So the coefficient of `x` in the expansion is `0`