Multiplying Polynomials

In this lesson, we will learn how to multiply two or more polynomials together. We will begin with the simplest case, which is to multiply a monomial by another monomial. Recall that multiplication is both commutative and associative. This means we can reorder our multiplication and we can regroup our multiplication and not change the product. To multiply a monomial by another monomial, we rearrange the multiplication in such a way that the coefficients are multiplied together and the variable parts are multiplied together. As we move into tougher scenarios, we see a monomial being multiplied by a non-monomial. In this case, we simply need to use our distributive property in order to multiply the monomial by each term of the polynomial. Additionally, we will also have to multiply two or more polynomials together when neither is a monomial. For this scenario, we will still use our distributive property. We can find the sum of each term of the first polynomial multiplied by each term of the second polynomial. Lastly, we will look at the special case scenario of multiplying two binomials together using FOIL. FOIL is an acronym for first terms, outside terms, inside terms, and last terms. FOIL gives us a quick road map for finding the product. It will give us the same result as just finding the sum of each term of the first polynomial multiplied by each term of the second polynomial.