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Factoring problem

  1. Mar 4, 2012 #1
    1. The problem statement, all variables and given/known data
    Factor the following: 16z^2 - 9x^2 - 12xy - 4y^2


    Solution of the problem is (4z - 3x -2y)(4z + 3x + 2y)

    3. The attempt at a solution

    I tried the following:

    16z^2 - 9x^2 - 12xy - 4y^2 = (4z - 3x)(4z + 3x) - 12xy - 4y^2 = (4z - 3x)(4z + 3x) - 4y(3x + y) /i also tried writing - 12xy - 4y^2 as -2y(6x + 2y)/

    16z^2 - 9x^2 - 12xy - 4y^2 = 16z^2 - 4y^2 - 9x^2 - 12xy = (4z - 2y)(4z + 2y) - 3x(3x + 4y)

    Thank you for your help!
     
  2. jcsd
  3. Mar 4, 2012 #2

    SammyS

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    Try working with the last three terms first.

    - 9x2 - 12xy - 4y2
     
  4. Mar 5, 2012 #3
    So the i get 16z^2 + (3x + 2y)(-3x - 2y). an i can write 16z^2 as (4z)(4z) now i need to somhowe fit (4z)(4z) in (3x + 2y)(-3x - 2y).
     
  5. Mar 5, 2012 #4
    I think i have solved it:

    16z^2 - 9x^2 - 12xy - 4y^2 = 16z^2 + 16z^2 + (-3x - 2y)(3x + 2y) = 16z^2 -1(3x + 2y)^2 = (4z + 3x +2y)(4z - 3x - 2y)

    Thank you for your help.

    Anyway i can rep you or something?
     
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