Question

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

Explanation:

Step1: Factor the given expression by grouping

Group the terms of \(2ax - 4ay + 3bx - 6by\) as \((2ax - 4ay)+(3bx - 6by)\).
Factor out the common factors from each group: \(2a(x - 2y)+3b(x - 2y)\).

Step2: Factor out the common binomial factor

Now, we can see that \((x - 2y)\) is a common binomial factor, so we factor that out: \((2a + 3b)(x - 2y)\).

Since one of the factors is given as \((2a + 3b)\), the other factor must be \((x - 2y)\).

Answer:

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