Answer:
8x^3 + 12x^2 - 2x - 3. This is the product in the form ax^3 + bx^2 + cx + d.
Explanation:
We are told that the first and smallest of three consecutive positive integers is (2x - 1).
The proper representation of the next integer is (2x - 1) + 2, or (2x + 1).
The third integer is (2x + 1) + 2, or (2x + 3).
The product of these three numbers is (2x - 1)(2x + 1)(2x + 3).
We need to multiply out this product. Start with (2x - 1)(2x + 1). This is a "special product" easily found: (2x)^2 - 1, or 4x^2 - 1.
Now we have only to multiply this (4x^2 -1) by (2x + 3). Using the FOIL method, we obtain:
8x^3 + 12x^2 - 2x - 3. This is the product in the form ax^3 + bx^2 + cx + d.