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Math Help - Hi, i need help to expand this binomial and write it simply

  1. #1
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    Cool Hi, i need help to expand this binomial and write it simply

    I need to expand this binomial fully and then write it as simply as possible thnx for help

    (2+4)^4 (^ meaning to the power of)
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Chez_ View Post
    I need to expand this binomial fully and then write it as simply as possible thnx for help

    (2+4)^4 (^ meaning to the power of)
    aren't you missing an x or something somewhere?
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  3. #3
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    oh yes sorry mis wrote it,
    should be (2+X)^4
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Chez_ View Post
    oh yes sorry mis wrote it,
    should be (2+X)^4
    there are two main ways to expand a binomial. one is using Pascal's triangle. the other is using the binomial theorem. i assume you learned the latter, since it is the method more generally taught.

    the binomial theorem basically says: (a + b)^n = \sum_{k = 0}^n {n \choose k} a^kb^{n - k}, you can switch a and b, and usually i prefer to do so, and write \sum_{k = 0}^n {n \choose k}a^{n - k}b^k

    and by {n \choose k} i mean _nC_k = C_k^n = \frac {n!}{k!(n - k)!}

    So (a + b)^4 = \sum_{k = 0}^4 {4 \choose k}a^{k}b^{n - k} = b^4 + 4ab^3 + 6a^2b^2 + 4a^3b + a^4

    can you continue?
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