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Math Help - Binomial coefficient second question

  1. #1
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    Binomial coefficient second question

    So I'm doing find the coefficient of x^4 in (3x-(1/x^2))^22

    I've done where a = 3x and b = 1/x^2

    (22)
    (K) (3x)^K (-1/x^2)^(22-K)

    (22)
    (K) (3^K) (x^K) (-1)^(22-K) x^-2(22-K) ----- I think this is where I've stuffed up

    (22)
    (K) (3^K) (-1)^(22-K).... not sure from here lol.

    Please help! Would be appreciated.
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  2. #2
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    nth term in a binomial expansion (a+b)^n is given by

    T(r+1) = nCr*a^(n-r)*b^r

    = 22Cr*(3)^(22-r)*(x)^(22-r)*(-1)^r*(1/x^2)^r

    Collect the terms containing x and simplify. Equate the power of x to 4 and find the value of r.
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  3. #3
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    Quote Originally Posted by brumby_3 View Post
    So I'm doing find the coefficient of x^4 in (3x-(1/x^2))^{22}

    I've done where a = 3x and b = 1/x^2
    Please help! Would be appreciated.
    find the coefficient x^4 in (3x-(1/x^2))^{22}

    (3x-(1/x^2))^{22}= _{22}C_k.(3x)^k.(x^{-2})^{(22-k)}.(-1)^{(22-k)}

    now, you need to find the value of k first.
    (x)^k.(x^{-2})^{(22-k)}=x^4



    ......hope it'll help........
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