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

2x⋅3x +3⋅3x

1 answer

To correctly distribute the expression \((2x + 3)(3x - 1)\), we use the distributive property (also known as the FOIL method for binomials).

Here's the step-by-step distribution:

  1. First, multiply the first term of the first binomial by the first term of the second binomial:

    • \(2x \cdot 3x = 6x^2\)

  2. Next, multiply the first term of the first binomial by the second term of the second binomial:

    • \(2x \cdot (-1) = -2x\)

  3. Then, multiply the second term of the first binomial by the first term of the second binomial:

    • \(3 \cdot 3x = 9x\)

  4. Finally, multiply the second term of the first binomial by the second term of the second binomial:

    • \(3 \cdot (-1) = -3\)

Putting it all together, we have: \[ 6x^2 - 2x + 9x - 3 \] Now combine like terms: \[ 6x^2 + 7x - 3 \]

Given the options you provided, the correct representation of the distribution is: \[ 2x \cdot 3x + 2x \cdot (-1) + 3 \cdot 3x + 3 \cdot (-1) \] This matches with the option: 2x⋅3x + 2x⋅−1 + 3⋅3x + 3⋅−1