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Math Help - Determine the coefficient of

  1. #1
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    Determine the coefficient of

    I am looking at the problem

    "Determine the coefficient of x4y6 in (2x + 3y)10"

    Ok I am a little confused here.

    Is this asking me to expand (2x + 3y)10 and then find the coefficent of that term in the result polynomial.

    Just lost here.

    Any guidance=very appreciated!
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  2. #2
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    Re: Determine the coefficient of

    Quote Originally Posted by ehpoc View Post
    I am looking at the problem

    "Determine the coefficient of x4y6 in (2x + 3y)10"

    Ok I am a little confused here.

    Is this asking me to expand (2x + 3y)10 and then find the coefficent of that term in the result polynomial.

    Just lost here.

    Any guidance=very appreciated!
    From the binomial theorem, the general term is ^nC_r (2x)^{10-r} (3y)^r = ^nC_r 2^{10-r} 3^r x^{10-r}y^r.

    Your job is to determine the value of r that gives x^4 y^6 and then use this value to evaluate the required coefficient.
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  3. #3
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    Re: Determine the coefficient of

    So I must look at the powers of x and y to determine r right?

    so that term would look like x^n-6 y^6 so that is the 7th term right?

    So the coefficient would be 10 choose 6?
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  4. #4
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    Re: Determine the coefficient of

    Quote Originally Posted by ehpoc View Post
    So I must look at the powers of x and y to determine r right?

    so that term would look like x^n-6 y^6 so that is the 7th term right?

    So the coefficient would be 10 choose 6?
    What about the contribution from the powers of 2 and powers of 3 ...??
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  5. #5
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    Re: Determine the coefficient of

    What about the contribution from the powers of 2 and powers of 3 ...??
    I don't know....lol I forgot my notes a home could you explain what I am missing?
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    Re: Determine the coefficient of

    Quote Originally Posted by ehpoc View Post
    I don't know....lol I forgot my notes a home could you explain what I am missing?
    I suggest you read post #2 with greater care and attention.
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  7. #7
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    Re: Determine the coefficient of

    Ok I get

    (10C6)(2x)^4(3y)^6

    =(10C6)(2^4)(3^6)x^4y^6

    correct?
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  8. #8
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    Re: Determine the coefficient of

    Quote Originally Posted by ehpoc View Post
    (10C6)(2x)^4(3y)^6
    =(10C6)(2^4)(3^6)x^4y^6
    correct?
    Technically the answer is just the coefficient:
    \binom{10}{6}(2^4)(3^6)
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