Which of the following is a factor of 36x² - 16y^2?
6x + 4y is a factor of 36x² - 16y².
The expression 36x² - 16y² can be factored using the difference of squares formula, which states that a² - b² = (a - b)(a + b). Here, it can be expressed as (6x)² - (4y)², leading to the factors (6x - 4y)(6x + 4y).
This choice does not correctly represent a factor of the given expression. Rearranging the terms does not yield a factor that corresponds to the difference of squares. The coefficients and variable arrangement do not satisfy the required conditions for factorization.
This is indeed a factor of the expression 36x² - 16y². It directly arises from the factored form (6x - 4y)(6x + 4y) and adheres to the difference of squares formula, confirming its validity as a factor.
This choice does not factor into the expression correctly. When expanded, 8x - 6y does not yield any combination that aligns with the original quadratics formed in the difference of squares, making it an incorrect option.
While this expression resembles a linear factor, it does not accurately correspond to the factors of 36x² - 16y². The coefficients do not align with the necessary components derived from the difference of squares formula.
Like the previous options, this expression does not factor the original expression correctly. The terms do not align with the derived factors from the difference of squares, thus rendering it an invalid choice.
In summary, the expression 36x² - 16y² can be factored into (6x - 4y)(6x + 4y), confirming that 6x + 4y is a valid factor. The other choices fail to satisfy the factorization requirement as derived from the difference of squares principle, highlighting the importance of recognizing the correct relationships among terms in polynomial expressions.
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