Final answer:
After multiplying the binomial (x - 4) with the trinomial (-3x² - 4x + 2), the equivalent expression is -3x³ + 8x² + 18x - 8. However, this expression does not match any of the provided answer choices, indicating a possible error. We cannot match the correct product to any of the given choices.
Step-by-step explanation:
The expression in question is the product of a binomial (x - 4) and a trinomial (-3x² - 4x + 2). To find the equivalent expression, we need to use the distributive property, also known as the FOIL method for binomials, to multiply each term of the first expression by each term of the second expression. Let's multiply them step by step:
- Multiply x by -3x²: -3x³.
- Multiply x by -4x: -4x².
- Multiply x by 2: 2x.
- Multiply -4 by -3x²: 12x².
- Multiply -4 by -4x: 16x.
- Multiply -4 by 2: -8.
Now, combine like terms:
- -3x³ remains as is since it is the only cubic term.
- Combine -4x² and 12x² to get 8x².
- Combine 2x and 16x to get 18x.
- -8 is the constant term and it remains as is.
Thus, the equivalent expression is -3x³ + 8x² + 18x - 8. However, this is not one of the listed options. It looks like there has been a mistake either in the multiplication process or in the provided options. Therefore, we cannot match the correct product to any of the given choices.