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Core 1 help?

Discussion in 'General Discussion' started by TheCenturion, 7 Mar 2010.

  1. TheCenturion

    Capodecina

    Joined: 18 Mar 2008

    Posts: 12,755

    Core 1 maths help?

    Thank you for anyone who answers this. :)

    Find the coefficient of x^6 in the expansion of (1+3x)^12

    By my reckoning that is the Pascal's Triangle number x 3x^6 x 1 ^6

    The Pascal's Triangle number is:

    (12 x 11 x 10 x 9 x 8 x 7) / (1 x 2 x 3 x 4 x 5 x 6) = 308

    so the answer is 924x^6 ?

    Also, to find the x^7 coefficient in the expansion of (1-2x)^15, is it just the same, only with a negative sign?

    Thanks :D
     
    Last edited: 7 Mar 2010
  2. bmi92

    Hitman

    Joined: 1 Jan 2010

    Posts: 994

    Have you been taught nCr thing? So it would be 12C6.

    12!
    ---- = 924
    6! (12-6!)
     
  3. TheCenturion

    Capodecina

    Joined: 18 Mar 2008

    Posts: 12,755

    Yeah, but we've been taught a much simpler formula for it.

    Instead of

    n!/r! (n-r!)

    You just do one simple fraction, but with lots of numbers it can get complicated as above!
     
  4. bmi92

    Hitman

    Joined: 1 Jan 2010

    Posts: 994

    That's what I did... ?
     
  5. bmi92

    Hitman

    Joined: 1 Jan 2010

    Posts: 994

    Also

    (12 x 11 x 10 x 9 x 8 x 7) / (1 x 2 x 3 x 4 x 5 x 6) = 308

    Is wrong? Its 924.
     
  6. TheCenturion

    Capodecina

    Joined: 18 Mar 2008

    Posts: 12,755

    308 x 3x^ 6 x 1 ^ 6 = 924 :)