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Binomial expansion question that I cannot fathom

  1. Dec 6, 2012 #1
    1. The problem statement, all variables and given/known data

    It says: Determine the coefficient of p4q7 in the expansion of (2p-q)(p+q)10.

    I can find the coefficient of p4q6 in the expansion of (p+q)10 but how am I to find it for (2p-q)(p+q)10???



    2. Relevant equations

    Binomial expansion formula.

    3. The attempt at a solution

    [Coefficient of p4q6 in the expansion of (p+q)10 = (10C6) x (p)4 x (q)6.]
     
  2. jcsd
  3. Dec 6, 2012 #2

    Ray Vickson

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    Write
    [tex] (2p-q)(p+q)^{10} = 2 p (p+q)^{10} - q (p+q)^{10},[/tex] then find the coefficients of p^4 q^6 in each term separately.
     
  4. Dec 6, 2012 #3
    But they're asking for the coefficient of p^4q^7, not p^4q^6. BUT 4 + 7 = 11 and 11 is not the power on the original bracket. The powers on p and q must add up to 11, but they can't over here.
     
  5. Dec 6, 2012 #4

    Ray Vickson

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    I have told you how I would do the problem if I had to.
     
  6. Dec 6, 2012 #5
    You did but they're not asking for what you're doing. They're asking for the coeff. of p^4q^7, not p^4q^6 which is what you're finding.
     
  7. Dec 7, 2012 #6

    Curious3141

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    Use Ray Vickson's method. For the binomial ##(p+q)^{10}##, find the coefficient of ##p^3q^7## for the first product, and ##p^4q^6## for the second product.

    What happens when you multiply the first product by ##2p##, and the second by ##q##? Now do the subtraction.
     
  8. Dec 8, 2012 #7
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