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Math Help - Expanding with binomial theorem

  1. #1
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    Expanding with binomial theorem

    Hi, I was working through some exercises and came to this:

    (x^2+y)^7

    I got an answer which starts out as:

    x^{14}+7x^{12}y+21x^{10}y^2....

    etc. etc.

    but the textbook answer begins:

    x^{14}+7x^{12}+21x^{10}y^2.....

    note the missing y from the " 7x^{12}" part.

    This seems kooky to me, am I wrong or is the book wrong? And if I'm wrong, what did I do wrong?
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  2. #2
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    You are correct. The book probably just has a typo.
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  3. #3
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    Thanks for that, I was hoping it was a typo.

    But I have a related question. I've continued in this exercise set and have another question about how to handle negatives, for example in the problem:

    (2x^2-y^2)^6

    The first time I expanded this, I got (2x^2)^6 + 6(2x^2)^5 (-y^2) + 15(2x^2)^4 (-y^2)^2 .....etc.

    but when I went to do the next step, I noticed that everything came out positive because of the (-y^2) thing.

    so I rewrote it as (2x^2)^6 + 6(2x^2)^5 *-(y^2) + 15(2x^2)^4 *-(y^2)^2.......etc.

    This gives the right answer, but it looks messy, and I'm not happy with it because I just pulled it out of my ear, so to speak.

    I guess my question is, Am I doing this correctly or should I go back and do some rereading?
    Last edited by spishak; December 17th 2008 at 11:15 AM. Reason: corrected a mistake
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