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

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The expression 16z^2 - 9x^2 - 12xy - 4y^2 factors to (4z - 3x - 2y)(4z + 3x + 2y). Several attempts to factor the expression involved rearranging terms and grouping, ultimately leading to the correct factorization. Participants discussed various methods, including factoring by grouping and recognizing patterns in the quadratic terms. The solution was confirmed through different approaches, emphasizing the importance of manipulating the last three terms effectively. The discussion concluded with expressions of gratitude for assistance in solving the problem.
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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!
 
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Government$ said:

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
 
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).
 
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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