Final answer:
After multiplying the binomials and then by the third term, the correct simplified product is 7.5x^4 - 21x^3 + 12x^2, which is not one of the provided options.
Step-by-step explanation:
To find the product of the binomials (4−5x)(1−0.5x)(3x^2), we will use the distributive property to multiply each term in the first binomial by each term in the second binomial and then by the third term.
First, multiply (4 - 5x) and (1 - 0.5x):
- 4 * 1 = 4
- 4 * (-0.5x) = -2x
- (-5x) * 1 = -5x
- (-5x) * (-0.5x) = 2.5x^2
Combining these terms, we get 4 - 2x - 5x + 2.5x^2 or 4 - 7x + 2.5x^2.
Now, multiply every term by 3x^2:
- 4 * 3x^2 = 12x^2
- (-7x) * 3x^2 = -21x^3
- 2.5x^2 * 3x^2 = 7.5x^4
The final product is 7.5x^4 - 21x^3 + 12x^2.
Thus, none of the given options (a), (b), (c), or (d) is correct. The product simplifies to 7.5x^4 - 21x^3 + 12x^2.