Which process involves multiplying the first, inner, outer, and last terms of two binomials?

The process that involves multiplying the first, inner, outer, and last terms of two binomials is known as FOIL. This acronym specifically helps in remembering the steps necessary to multiply two binomials effectively.

When you apply FOIL, you systematically execute the multiplication in the following order:

1. First: Multiply the first terms of each binomial.
2. Outer: Multiply the outer terms.
3. Inner: Multiply the inner terms.
4. Last: Multiply the last terms of each binomial.

This method ensures that all the necessary product combinations are accounted for when expanding the expression. By following these steps, you arrive at a single trinomial or polynomial that represents the product of the two binomials.

In contrast, factoring is the process of breaking down a polynomial into its component factors, and the distributive property involves one term being multiplied by each term inside parentheses. Polynomial long division deals with dividing one polynomial by another and is a more complex process not directly related to the multiplication of binomials. Thus, FOIL is the precise term that encapsulates this specific multiplication method.