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Math Help - binomial theorem

  1. #1
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    binomial theorem

    use the binomial theorem to complete this expansion.

    (3x + 2y)^4 = 81x^4 + 216x^3y + .....
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  2. #2
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    What is it that you are having troubles with? You have a formula .. all you have to do is plug it in..

    (a+b)^n = \sum_{k=0}^n {n \choose k} a^{n-k}b^{k} = {n \choose 0}a^nb^0 + {n \choose 1}a^{n-1}b^1 + \cdots + {n \choose n}a^0b^n
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  3. #3
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    Hello, exclusiive!

    If you know the Binomial Theorem, it's straight-forward.
    Exactly where is your difficulty?


    Use the binomial theorem to complete this expansion:
    . . . (3x + 2y)^4 \:=\: 81x^4 + 216x^3y + \hdots

    (3x+2y)^4 \;=\;{4\choose4}(3x)^4(2y)^0 + {4\choose3}(3x)^3)(2y)^1 + {4\choose2}(3x)^2(2y)^2 +  {4\choose1}(3x)^1(2y)^3 + {4\choose0}(3x)^0(2y)^4

    . . . . . and crank it out.

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