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Math Help - Determine the constant term in.

  1. #1
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    Determine the constant term in.

    Determine the constant term in.
    idk how to solve it
    Last edited by skeeter; October 31st 2012 at 04:57 AM.
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  2. #2
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    Re: Determine the constant term in.

    each term in a binomial expansion is of the form ...

    \binom{n}{k} a^{n-k} b^k

    In this case, n = 21 ... the value of k will be such that the variable factors cancel.

    \binom{21}{18} (3x^6)^3\left(\frac{5}{x}\right)^{18}
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    Re: Determine the constant term in.

    i did not get it, i dont think i really understand what they want me to answer, with other words i maybe dont understand problem... im confused
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    Re: Determine the constant term in.

    Quote Originally Posted by Petrus View Post
    i did not get it, i dont think i really understand what they want me to answer, with other words i maybe dont understand problem... im confused
    1. have you learned the binomial theorem?

    2. do you understand that a constant term has no variable factors?
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    Re: Determine the constant term in.

    Quote Originally Posted by skeeter View Post
    1. have you learned the binomial theorem?

    2. do you understand that a constant term has no variable factors?
    hi!
    We have not come here yet, but I want to study in advance. I did read but did not understand clearly i dont like my book
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    Re: Determine the constant term in.

    Quote Originally Posted by Petrus View Post
    We have not come here yet, but I want to study in advance. I did read but did not understand clearly i dont like my book
    your book is not the sole source of knowledge. seek and ye shall find ...

    Binomial Theorem (part 1) | Precalculus | Khan Academy
    Thanks from Petrus
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    Re: Determine the constant term in.

    ok i did watch and i kinda understand but idk how in my problem to get out the constant term :S
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    Re: Determine the constant term in.

    I showed you how in post #2.
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    Re: Determine the constant term in.

    A constant terms comes out when a^n-k * b^k is a constant, and does not involve any variables. In your case, the binomial expansion has only one variable, x. That means, in (3x^6)^n - k * (5/x)^k does not contain any x. For it to happen, when n = 21, you need to equate the power of x to zero, since x^0 = 1, is a constant, and other powers yield terms with x, and so, not a constant term.

    (x^6)^21 - k * (1/x)^k = x^0
    (x^6)^21 - k * (x^-1)^k = x^0
    (x^6)^21 - k * x^-k = x^0
    x^(6(21-k) - k) = x^0

    Equating coefficients, you get k = 18, which is what he used to get the constant term above.

    Salahuddin
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    Re: Determine the constant term in.

    I solved this problem forgot to say it ty anyway
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