SOLUTION: Hi, I am resubmitting this question, as it might be confusing. Determine the constant term in the expansion of {{{(2x-2/5x^2)^8.}}} I am doing this math independently. I h

Algebra ->  Algebra  -> Permutations -> SOLUTION: Hi, I am resubmitting this question, as it might be confusing. Determine the constant term in the expansion of {{{(2x-2/5x^2)^8.}}} I am doing this math independently. I h      Log On

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Question 72469: Hi, I am resubmitting this question, as it might be confusing.
Determine the constant term in the expansion of
%282x-2%2F5x%5E2%29%5E8.
I am doing this math independently. I have looked through my
textbooks, but cannot find what a consant term is. I have
expanded this by binomial expansion but there is not one constant
term in the solution as all constants are differnt numbers with
differnt x values.
Thank you
Kristen
Answer by psbhowmick(489) About Me  (Show Source):
You can put this solution on YOUR website!
In the binomial expansion of %28a%2Bb%29%5En the r-th term is given by nC%5Br%5Da%5E%28n-r%29b%5Er when 'n' is a positive integer.
Here, a+=+2x, b+=+-2%2F5x%5E2, n+=+8.
Hence, the r-th term is
8C%5Br%5D%282x%29%5E%288-r%29%28-2%2F5x%5E2%29%5Er
= %28-1%29%5Er+8C%5Br%5D%282%5E%288-r%29%282%2F5%29%5Er%29x%5E%288-r%29x%5E%28-2r%29

Thus constant term is that one for which power of x is zero i.e. 8 - 3r = 0.
This gives r = 8/3. But r should be integer.
So you are correct!
This binomial expansion doesn't have a constant term if you have typed correctly.