# Binomial expansion

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#1
{2+x}^-2 how would you expand this in ascending powers of 1/x ?
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1 week ago
#2
Take x out of the bracket so it's x^-2 (1 +2/x)^-2 then expand that
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#3
(Original post by Meowstic)
Take x out of the bracket so it's x^-2 (1 +2/x)^-2 then expand that
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
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1 week ago
#4
(Original post by Sidd1)
{2+x}^-2 how would you expand this in ascending powers of 1/x ?
Do you mind posting a pic of the original question? Just because it's a bit unusual.
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1 week ago
#5
(Original post by Sidd1)
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
You want to expand in factors of 1/x so you make the term in the bracket into 1 + a(1/x)
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#6
(Original post by Sir Cumference)
Do you mind posting a pic of the original question? Just because it's a bit unusual.
Sure
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#7
(Original post by RDKGames)
This question doesn't make sense at A-Level context. Binomial expansion is done about the point at A-Level, so naturally no matter how you rewrite the end result, it will always be an expansion in increasing powers of , not .

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

If this question genuinely wants you to obtain the expansion in increasing powers of , then the expansion needs to happen about the point . This is way beyond A-Level and known as 'Laurent series'.
Umm okayyyyyyy that's weird.
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1 week ago
#8
(Original post by Sidd1)
Umm okayyyyyyy that's weird.
Oh ignore it, I overlooked something in the analysis. Factoring out x^(-2) is fine. Only issue I have with this question is that the (x+2)^(-2) is defined at x=0 but the expansion obviously isn't. So you should be careful when it comes to stating the region of validity of this expansion.
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1 week ago
#9
There's no issue with the question. It's perfectly fine.
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