Binomial expansion

Take x out of the bracket so it's x^-2 (1 +2/x)^-2 then expand that

{2+x}^-2 how would you expand this in ascending powers of 1/x ?

How would you know what to factor out? Usually, I would take the 2 out and then have (1+1/2x)^-2. An explanation would be really helpful

Do you mind posting a pic of the original question? Just because it's a bit unusual.

This question doesn't make sense at A-Level context. Binomial expansion is done about the point $x=0$ at A-Level, so naturally no matter how you rewrite the end result, it will always be an expansion in increasing powers of $x$, not $\frac{1}{x}$.

Even if you 'take x out of the bracket' you will ultimately have a series that increases in powers of $x$.

If this question genuinely wants you to obtain the expansion in increasing powers of $\frac{1}{x}$, then the expansion needs to happen about the point $x=\infty$. This is way beyond A-Level and known as 'Laurent series'.

Umm okayyyyyyy that's weird.