Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.

  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...
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook