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Math Help - binomial expanding

  1. #1
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    binomial expanding

    I'm supposed to use the Binomial Theorem to simplify the two following problems

    (X-2)^4 (Answer: X^4-8x^3+24X^2-32X+16

    and...

    (2+3s)^6 (Answer: 64+576S+2160S^2+4320S^3+4860S^4+2916S^5+729S^6)

    But I'm completely stumped, I have absolutely no idea how to use the binomial theorem and am in need of some step by step help. I'd appreciate it tremendously.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Samurai Karasu View Post
    I'm supposed to use the Binomial Theorem to simplify the two following problems

    (X-2)^4 (Answer: X^4-8x^3+24X^2-32X+16
    The binomial theorem states

    (a+b)^n=\sum_{k=0}^{n}\binom{n}{k}(a)^{n-k}(b)^k

    so we we identify the parts a=x b=(-2) and n=4


    (x-2)^4=\sum_{k=0}^{4}\binom{4}{k}(x)^{4-k}(-2)^k

    Now we let k=0,1,2,3,4

    \sum_{k=0}^{4}\binom{4}{k}(x)^{4-k}(-2)^k=\binom{4}{0}(x)^{4-0}(-2)^0+\binom{4}{1}(x)^{4-1}(-2)^1
    +\binom{4}{2}(x)^{4-2}(-2)^2+\binom{4}{3}(x)^{4-3}(-2)^3+\binom{4}{4}(x)^{4-4}(-2)^4=

    x^4-8x^3+24x^2-32x+16

    See what you can do with the next one.
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  3. #3
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    I seriously just got it!

    The only thing I had to think about was you need to use Pascal's Triangle to put coefficents in front of the numbers, but otherwise I finally got it! Thank you tremendously my man, I think I might be able to do good on that test tomorrow thanks to you.
    Last edited by ThePerfectHacker; May 21st 2008 at 01:17 PM.
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