Results 1 to 3 of 3

Math Help - Factorisation

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    27

    Factorisation

    Factorise:

    (xy+1)^4 - 4xy(xy+1)^2 - (x^2 - y^2)^2

    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Aug 2008
    Posts
    530

    Reply

    Quote Originally Posted by muks View Post
    Factorise:

    (xy+1)^4 - 4xy(xy+1)^2 - (x^2 - y^2)^2

    Thank you.
    (xy+1)^4 - 4xy(xy+1)^2 - (x^2 - y^2)^2

    As you see, (xy+1)^2 comes twice, so, Complete the square

    =[(xy+1)^2]^2-2(2xy)(xy+1)^2+(2xy)^2-(2xy)^2-(x^2-y^2)^2

    =[(xy+1)^2-(2xy)]^2-(2xy)^2-(x^2-y^2)^2

    =[x^2y^2+1+2xy-2xy]^2-4x^2y^2-[(x^2)^2+(y^2)^2-2x^2y^2]

    =(x^2y^2+1)^2-[4x^2y^2+(x^2)^2+(y^2)^2-2x^2y^2]

    =(x^2y^2+1)^2-[(x^2)^2+(y^2)^2+2x^2y^2]

    =(x^2y^2+1)^2-(x^2+y^2)^2

    =(x^2y^2+1+x^2+y^2)(x^2y^2+1-x^2-y^2)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2008
    Posts
    27
    I agree with the answer provided, but the answer in the book is (x+1)(x-1)(y+1)(y-1)(x^2+1)(y^2+1)

    How did they obtain?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. factorisation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 23rd 2010, 09:39 AM
  2. factorisation
    Posted in the Algebra Forum
    Replies: 9
    Last Post: December 29th 2009, 01:45 PM
  3. Further factorisation
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 24th 2009, 07:29 PM
  4. Factorisation
    Posted in the Algebra Forum
    Replies: 2
    Last Post: November 5th 2008, 03:54 AM
  5. Factorisation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 10th 2006, 12:01 AM

Search Tags


/mathhelpforum @mathhelpforum