Question

Which line shows the correct and complete distribution for the problem below?

(2x+3)(3x−1)

(1 point)
Responses

2x⋅3x−2x⋅−1−3⋅3x−3⋅−1
2 x times 3 x minus 2 x times negative 1 minus 3 times 3 x minus 3 times negative 1

2x⋅3x +3⋅3x
2x⋅3x +3⋅3x

2x⋅3x+2x⋅−1+3⋅3x+3⋅−1
2 x times 3 x plus 2 x times negative 1 plus 3 times 3 x plus 3 times negative 1

2x⋅3+3x⋅−1
2 x times 3 plus 3 x times negative 1

Answer 1

To correctly distribute the expression \((2x + 3)(3x - 1)\), we can follow the distributive property, often referred to as the FOIL method for binomials, which stands for First, Outer, Inner, Last.

For the expression \((2x + 3)(3x - 1)\), we would get the following terms:

1. First: \(2x \cdot 3x = 6x^2\)
2. Outer: \(2x \cdot (-1) = -2x\)
3. Inner: \(3 \cdot 3x = 9x\)
4. Last: \(3 \cdot (-1) = -3\)

This results in:

\[
6x^2 - 2x + 9x - 3
\]

Combining the like terms gives you:

\[
6x^2 + 7x - 3
\]

Now, looking at the provided options for distribution, the correct and complete distribution should represent each of those steps clearly.

The correct line that shows the complete distribution is:

**2x⋅3x + 2x⋅−1 + 3⋅3x + 3⋅−1**

This option includes all necessary multiplicative steps of the distribution. Therefore, this is the correct response.