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Math Help - Finding a term in a Binomial Expansion

  1. #1
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    Post Finding a term in a Binomial Expansion

    Good evening forum I am having a problem with the following problem any help would be appreciated:


    thank you , AC
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by AlgebraicallyChallenged View Post
    Good evening forum I am having a problem with the following problem any help would be appreciated:


    thank you , AC
    use the binomial expansion formula for (x + y)^8

    we have (x + y)^8 = \sum_{k = 0}^8 {8 \choose k}x^{8 - k}y^k

    if we choose x = a and y = -b^3 we realize that we want the term where we have y^3...that's where k = 3

    this is the term {8 \choose 3}x^5y^3


    note that {n \choose k} = _nC_k = \frac {n!}{k!(n - k)!}
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    Quote Originally Posted by AlgebraicallyChallenged View Post
    Good evening forum I am having a problem with the following problem any help would be appreciated:


    thank you , AC
    (a-b^3)^8 = {8\choose0}a^8 + {8\choose1}a^7(-b^3) + {8\choose2}a^6(-b^3)^2 + {8\choose3}a^5(-b^3)^3 + ...

    see the term you need to find?
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