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

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In summary, the given expression can be factored as (4z + 3x + 2y)(4z - 3x - 2y). The attempt at a solution involved trying to fit (4z)(4z) into (3x + 2y)(-3x - 2y), which resulted in the correct factorization of the expression. No output was provided before the summary.
  • #1
Government$
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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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  • #2
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
 
  • #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).
 
  • #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?
 

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

1. What is the general method for factoring a polynomial expression?

The general method for factoring a polynomial expression involves finding the common factors among the terms, using the distributive property to group terms, and then factoring each group using techniques such as the difference of squares, trinomial factoring, or grouping.

2. How do I factor a polynomial expression with four terms?

To factor a polynomial expression with four terms, you can first look for common factors among the terms. If there are no common factors, you can try grouping the terms into two pairs and factoring out the greatest common factor from each pair. You can also use the difference of squares or trinomial factoring techniques if applicable.

3. Can the polynomial expression 16z^2 - 9x^2 - 12xy - 4y^2 be factored?

Yes, the polynomial expression 16z^2 - 9x^2 - 12xy - 4y^2 can be factored. It can be factored into (4z - 3x)(4z + 3x) - 4y(3x + z).

4. What are the common factors in the expression 16z^2 - 9x^2 - 12xy - 4y^2?

The common factor in the expression 16z^2 - 9x^2 - 12xy - 4y^2 is (4z - 3x).

5. Is there a shortcut or easier way to factor a polynomial expression?

There is no one specific shortcut or easier way to factor a polynomial expression, as it depends on the specific expression and the techniques that can be applied. However, it may be helpful to first look for common factors and then apply known factoring techniques to simplify the expression.

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