Factoring 16z^2 - 9x^2 - 12xy - 4y^2

[Government$]

Homework Statement

Factor the following: 16z^2 - 9x^2 - 12xy - 4y^2


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

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!

 

[SammyS]

Homework Statement

Factor the following: 16z^2 v


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

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!

Try working with the last three terms first.

- 9x² - 12xy - 4y²

 

[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).

 

[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)

Thank you for your help.

Anyway i can rep you or something?