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 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 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

Answer 1

The correct and complete distribution for the expression \((2x+3)(3x−1)\) involves multiplying each term in the first parenthesis by each term in the second parenthesis.

Let's break down the expression step-by-step:

1. Multiply \(2x\) by \(3x\): \(2x \cdot 3x = 6x^2\)
2. Multiply \(2x\) by \(-1\): \(2x \cdot -1 = -2x\)
3. Multiply \(3\) by \(3x\): \(3 \cdot 3x = 9x\)
4. Multiply \(3\) by \(-1\): \(3 \cdot -1 = -3\)

Now, combining these results gives:

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

Looking at the provided responses, the line that shows the correct and complete distribution is:

**2x⋅3x + 2x⋅−1 + 3⋅3x + 3⋅−1**

This corresponds to the mathematical operations we performed and accurately reflects the distribution process.