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Finding a Coefficient in an Expansion (n-j is negative?)

  1. Oct 15, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the coefficient of x8 in the expansion of (x2-3)7

    2. Relevant equations

    This one:

    (n n-j) an-jxj



    3. The attempt at a solution
    Hi!
    Well, I know that
    x= x2
    a= -3
    n= 7
    and apparently, j=8.

    This is what confuses me. n-j is a negative number.. how would that even work?? My guess is that the x2 has to do with it somehow... I'm thinking because the x is squared, then n wouldn't be 7.

    Please help!
    I wrote this on wolfram alpha because I was like.. "is this possible or is it just a typo?" and it gave me an answer!

    Thank you!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 15, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    No, no. (a+b)^n=sum over j of (n j)a^j*b^(n-j). Put a=x^2 and b=(-3). You are likely getting confused because you are using the same symbol x for two different things. Saying x=x^2 is just silly.
     
  4. Oct 15, 2013 #3
    Hmm well.. that's how my professor did it.

    So after trying multiple times with different values for n and j, I got the right one. I ended up using n=7 and j=4. At first I tried n=14 and j=8. Nope. Then, I tried n=14 and j=4. Nope. Then, I tried n=7 and j=4! It worked... I'm still not so sure of why. I think the n is seven like normal.. but if I put 8 as j, then x will be to the power of 16. So I tried 4 and it worked..

    Thanks.
     
  5. Oct 15, 2013 #4

    Office_Shredder

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    Staff Emeritus
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    Gold Member

    rakeru, if I asked you to calculate the power of y4 in (y-3)7, do you see why this is the same as your original question?
     
  6. Oct 15, 2013 #5
    In that case, j would be just four, right?
     
  7. Oct 15, 2013 #6

    Dick

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    Homework Helper

    Of course it would. Same for your original problem if you separate the two uses of x.
     
  8. Oct 16, 2013 #7
    Oh my god! Yes! I see!!

    Thank you!!!

    I wonder why my teacher did it like that, though.

    Thanks! :)
     
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