Results 1 to 3 of 3

Math Help - Binomial expansion terms

  1. #1
    Member Greengoblin's Avatar
    Joined
    Feb 2008
    From
    UK
    Posts
    182

    Binomial expansion terms

    When we expand a binomial, (x+y)^n I understand how the coefficient of x^r will be ^nC_r, but not why the terms group together as they do in the form x^{n-r}y^r.

    Why is this the case and not x^ry^r for example?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Greengoblin View Post
    When we expand a binomial, (x+y)^n I understand how the coefficient of x^r will be ^nC_r, but not why the terms group together as they do in the form x^{n-r}y^r.

    Why is this the case and not x^ry^r for example?
    Try expanding using concrete value of n like n = 2, n = 3, n = 4. Then you should see that the sum of the powers has to add up to n.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member Greengoblin's Avatar
    Joined
    Feb 2008
    From
    UK
    Posts
    182
    Thanks I've tried expanding for n=2,3,4, using the formula, and doing algebraically, and got the expected expressions in both cases, but still can't see why the powers of x and y in each term must add to n.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Avoiding Large Number of Terms in Equation Expansion
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: April 28th 2011, 12:59 PM
  2. [SOLVED] Neglecting terms (and binomial expansion)
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: July 2nd 2010, 09:41 AM
  3. last terms of expansion
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: November 9th 2009, 01:18 AM
  4. First Four nonzero terms in power series expansion
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: July 29th 2009, 12:44 PM
  5. Replies: 6
    Last Post: May 1st 2009, 12:37 PM

Search Tags


/mathhelpforum @mathhelpforum