# Factoring problem

1. Mar 4, 2012

### Government$1. The problem statement, all variables and given/known data Factor the following: 16z^2 - 9x^2 - 12xy - 4y^2 Solution of the problem is (4z - 3x -2y)(4z + 3x + 2y) 3. The attempt at a solution I tried the following: 16z^2 - 9x^2 - 12xy - 4y^2 = (4z - 3x)(4z + 3x) - 12xy - 4y^2 = (4z - 3x)(4z + 3x) - 4y(3x + y) /i also tried writing - 12xy - 4y^2 as -2y(6x + 2y)/ 16z^2 - 9x^2 - 12xy - 4y^2 = 16z^2 - 4y^2 - 9x^2 - 12xy = (4z - 2y)(4z + 2y) - 3x(3x + 4y) Thank you for your help! 2. Mar 4, 2012 ### SammyS Staff Emeritus Try working with the last three terms first. - 9x2 - 12xy - 4y2 3. Mar 5, 2012 ### Government$

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).

4. Mar 5, 2012

### Government\$

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)