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Can anyone please help me to generalize and prove this if it is valid?

  1. Apr 22, 2012 #1
    X^4-(X^3)y+(X^2)(y^2)-x(y^3)+y^4= (x+y)^4-5xy(x+y)^2+5(xy)^2

    x^6-(x^5)y+(X^4)(y^2)-(X^3)(y^3)+(X^2)(y^4)-x(y^5)+y^6=(x+y)^6-7xy(x+y)^4 +14((xy)^2)(x+y)^2 - 7(xy)^3

    ....................
    If n is an odd prime then prove,

    x^n-1 - X^(n-2).y+..........-x.y^(n-2)+y^(n-1) = (x+y)^n-1 - nxy(x+y)^(n-3) +..........(-1)^((n-1)/2) . n .(xy) ^ ((n-1)/2)


    Thank you very much in advance for your assistance.
     
  2. jcsd
  3. Apr 22, 2012 #2


    Your post is very difficult to read in ASCII...I even didn't try. My advice: learn how to post here in LaTeX or else

    attach some document, preferably PDF, where mathematical stuff appears decently.

    DonAntonio
     
  4. Apr 23, 2012 #3
    I think this has been posted before recently but, for the love of me, I can't find the original post.

    And I believe the suggestion was to learn about the binomial theorem; then try to expand (x+y)^4 and (x+y)^6.
     
  5. Jun 27, 2012 #4
    that's simple re arrangement of binomial expansions. for general proof, try general form of binomial expansions. you will get it easily.
     
  6. Jul 3, 2012 #5
    Or else use the "sup" and "sub" tags to create superscripts and subscripts:

    [noparse]xy xy[/noparse]

    xy xy
     
  7. Aug 13, 2012 #6
    Got the point. Thanks every one...
     
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