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