Final answer:
To find the expression representing the product of two polynomials, one must multiply each term in the first polynomial by each term in the second polynomial and combine like terms. The correct expression is required for the specific answer.
Step-by-step explanation:
The expression that represents the product of 3 + 2x - 1 and 24 - 2x^{3} + 3 requires applying the distributive property to multiply each term in the first expression by each term in the second expression.
This operation is commonly known as FOIL (First, Outside, Inside, Last) when dealing with binomials, but it can also be applied to polynomials with more than two terms.
First, we multiply the first terms. Then we multiply the outside terms, followed by the inside terms, and finally, the last terms of both expressions. We combine like terms, if any, to obtain the final simplified result.
It's important to note that the expression provided in the question seems to contain possible typos or incorrect exponents. As a result, without the correct expression, we can't provide the specific answer here.