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⋅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 find the correct distribution of the expression (2x + 3)(3x - 1), we need to apply the distributive property (also known as the FOIL method for binomials):

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

Thus, the complete distribution will be:

• \( 2x \cdot 3x \)
• \( 2x \cdot (-1) \)
• \( 3 \cdot 3x \)
• \( 3 \cdot (-1) \)

Putting it all together, the expression is:

\[ 2x \cdot 3x + 2x \cdot (-1) + 3 \cdot 3x + 3 \cdot (-1) \]

So, the correct choice from your options would be:

2x⋅3x + 2x⋅−1 + 3⋅3x + 3⋅−1