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Math Help - find the coeffiecient

  1. #1
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    find the coeffiecient

    Find the coefficient of x4 in the expansion of (3x - 2)6
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  2. #2
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    Hello, maptorren!

    I must assume you're familiar with the Binomial Expansion.


    Find the coefficient of x^4 in the expansion of (3x-2)^6
    The term we seek is: . {6\choose4}(3x)^4(\text{-}2)^2 \;=\;15(81x^4)(4) \;=\;4860x^4

    The coefficient is 4860.

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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by maptorren View Post
    Find the coefficient of x4 in the expansion of (3x - 2)6
    Use the binomial theorem:

    (a-b)^4=1a^6(-b)^0+\frac{6}{1}a^5(-b)^1+\boxed{\frac{6\cdot5}{1\cdot2}a^4(-b)^2}

    Substitute 3x for a, and 2 for b

    Soroban is correct.. 4860 is your coefficient.
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  4. #4
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    Using the factorial form of the binomial theorem, you want to find the 3rd term of (3x-2)^6.

    (3x-2)^6=\sum_{k=0}^{6} \frac{6!}{(6-k)!k!}\ \  (3x)^{6-k}(-2)^k

    Find the 3rd term when k=2,

    \frac{6!}{(6-2)!2!}\ \ (3x)^{6-2}(-2)^2=\frac{6\cdot5\cdot4\cdot3\cdot2\cdot1}{4\cdot  3\cdot2\cdot1\cdot2\cdot1}(3x)^4(4)=15\cdot81x^4\c  dot4=4860x^4
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  5. #5
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    find the coeffiecient

    what about when you have something like find the coefficient of x^4 in the expansion of (3x -1/x)^6.
    Last edited by maptorren; July 29th 2008 at 11:55 AM. Reason: Urgent
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  6. #6
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    Please help

    how would i solve this porblem
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