Question

cd: factor by gcf and grouping
determine the other factor for (2ax - 4ay + 3bx - 6by) if one of the factors is ((2a + 3b)).
a ((x^2 - 4y^2))
b ((x - 2y)^2)
c ((x - 2y))
d ((x + 2y))

Explanation:

Step1: Group the terms

Group the first two terms and the last two terms: \((2ax - 4ay)+(3bx - 6by)\)

Step2: Factor out GCF from each group

Factor out \(2a\) from the first group and \(3b\) from the second group: \(2a(x - 2y)+3b(x - 2y)\)

Step3: Factor out the common binomial factor

Now, we can see that \((x - 2y)\) is a common factor, so we factor that out: \((2a + 3b)(x - 2y)\)
Since one of the factors is \((2a + 3b)\) (similar to the given \((2a+3b)\) in the problem context), the other factor is \((x - 2y)\)

Answer:

C. \((x - 2y)\)