Find the middle terms of this binomial expansion

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Homework Help Overview

The problem involves finding the middle terms of the binomial expansion of the expression (4 - x^3)^7. The original poster expresses uncertainty about whether there is a single middle term or two middle terms due to the total number of terms in the expansion.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the total number of terms in the expansion and question the definition of the middle term(s). There is consideration of whether the middle term exists or if it consists of two terms, specifically the 4th and 5th terms.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the question. Some guidance is provided regarding the potential for two middle terms, but no consensus is reached on the clarity of the original question.

Contextual Notes

There is mention of specific terms in the expansion that may not be included in the original poster's consideration, indicating a possible oversight in the problem setup.

songoku
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Homework Statement
Find the middle terms of ##\left( 4 - x^3 \right)^7##
Relevant Equations
Binomial expansion
I know how to expand it. My question is: the expansion has 8 terms so what would be the middle term? Will the answer be "the expansion has no middle term"?

Or maybe seeing the phrase of the question (middle terms), there will be two answers (the 4th and 5th term)?

Thanks
 
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I assume the problem suggests all the expansion terms except obvious ##4^7## and ##-x^{21}##.
 
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Thank you very much anuttarasammyak
 
songoku said:
Homework Statement:: Find the middle terms of ##\left( 4 - x^3 \right)^7##
Relevant Equations:: Binomial expansion

I know how to expand it. My question is: the expansion has 8 terms so what would be the middle term? Will the answer be "the expansion has no middle term"?

Or maybe seeing the phrase of the question (middle terms), there will be two answers (the 4th and 5th term)?

Thanks
I suspect the intent of the questioner is to ask for the 4th and 5th terms as you suggested. However, the wording is not all that clear so @anuttarasammyak may indeed be correct.
 
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Thank you very much SammyS
 

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