For all values of x and y, which expression is equivalent to 8x + 6y?

Question

Question 4 options:

4(2x + 3y)

2x + 3y

2(4x + 3y)

3(4x + 2y)

Answer 1

To determine which expression is equivalent to \(8x + 6y\), we can evaluate each of the provided options.

1. Option 1: \(4(2x + 3y)\) \[ 4(2x + 3y) = 4 \cdot 2x + 4 \cdot 3y = 8x + 12y \] This does not equal \(8x + 6y\).

2. Option 2: \(2x + 3y\) This is simply \(2x + 3y\) and does not equal \(8x + 6y\).

3. Option 3: \(2(4x + 3y)\) \[ 2(4x + 3y) = 2 \cdot 4x + 2 \cdot 3y = 8x + 6y \] This is equal to \(8x + 6y\).

4. Option 4: \(3(4x + 2y)\) \[ 3(4x + 2y) = 3 \cdot 4x + 3 \cdot 2y = 12x + 6y \] This does not equal \(8x + 6y\).

The only expression that is equivalent to \(8x + 6y\) is:

Option 3: \(2(4x + 3y)\).