Question

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

(2x+3)(3x−1)
(1 point)
Responses

2x⋅3x +3⋅3x

2x⋅3+3x⋅−1

2x⋅3x+2x⋅−1+3⋅3x+3⋅−1

2x⋅3x−2x⋅−1−3⋅3x−3⋅−1

Answer 1

To find the correct and complete distribution of the expression \((2x+3)(3x−1)\), we can use the distributive property (also known as the FOIL method for binomials).

We will multiply each term in the first parentheses \( (2x + 3) \) by each term in the second parentheses \( (3x - 1) \):

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

Now we can combine these results:

\[
(2x + 3)(3x - 1) = 6x^2 + (-2x + 9x) + (-3) = 6x^2 + 7x - 3
\]

Now, we can match this distribution with one of the response options. The one that shows the complete distribution correctly is:

**2x⋅3x + 2x⋅(-1) + 3⋅3x + 3⋅(-1)**

So, the correct response is:

**2x⋅3x + 2x⋅−1 + 3⋅3x + 3⋅−1**