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

Question

(2x+3)(3x−1)
(1 point)
Responses

2x⋅3x +3⋅3x
2x⋅3x +3⋅3x

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

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⋅3x−2x⋅−1−3⋅3x−3⋅−1

Answer 1

To correctly distribute the expression (2x + 3)(3x - 1), we apply the distributive property (FOIL method for binomials):

1. Multiply the first terms: \(2x \cdot 3x = 6x^2\)
2. Multiply the outer terms: \(2x \cdot (-1) = -2x\)
3. Multiply the inner terms: \(3 \cdot 3x = 9x\)
4. Multiply the last terms: \(3 \cdot (-1) = -3\)

Now, combine all these results:

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

Combining like terms, we get:

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

So, the line that shows the correct and complete distribution is:

2x⋅3x + 2x⋅−1 + 3⋅3x + 3⋅−1

This is option 3:

2x⋅3x + 2x⋅−1 + 3⋅3x + 3⋅−1