Question 5

6x + 4y is a factor of 36x² - 16y².

The expression 36x² - 16y² can be factored as a difference of squares, which reveals that 6x + 4y is one of its factors.

A) 4x + 6y

This option is not a factor because when tested with the difference of squares method, it does not yield a valid factorization of 36x² - 16y². The coefficients do not align with the necessary terms derived from the factorization process.

B) 6x + 4y

This option is correct as it can be derived from the factorization of 36x² - 16y². By rewriting the expression as (6x)² - (4y)², we can apply the difference of squares formula, yielding (6x - 4y)(6x + 4y), confirming that 6x + 4y is indeed a factor.

C) 8x - 6y

This choice does not factor into the expression 36x² - 16y². The coefficients do not correspond to the squares of integer multiples that would result from the factorization of the original expression.

D) 9x - 4y

While this option appears to be related to the original expression, it is not a valid factor. The structure does not satisfy the necessary algebraic conditions to be part of the factorization of 36x² - 16y².

E) 18x - 8y

This option is also incorrect as it does not align with the factorization of the original expression. The coefficients do not match the required terms to result from the expression's factorization.

Conclusion

The correct answer, 6x + 4y, is a direct result of applying the difference of squares formula to 36x² - 16y², while the other options fail to satisfy the necessary conditions for being factors. Each of the incorrect choices either misaligns with the algebraic structure or does not yield valid factors of the given expression.