# Week 5 – Math 10 – Multiplication of Polynomials

Compared to last year where we only did the multiplication of monomials and there was one way that we could evaluate the expression. However, with the multiplication of polynomials, there are a couple of ways. Before moving on to two of the ways of evaluating the polynomial, here is a short review of them.

What are polynomials?

It is an expression that has more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s). There are four types of polynomials; a monomial, binomial, trinomial, and a polynomial. A monomial means that there is only one term when in a binomial there are two terms. So that means that a trinomial has three terms and polynomials have anywhere more than four terms. Polynomials can’t have an exponent of the negative integer in the numerator. As well as the variable can’t be in the denominator.

The first way of evaluating a problem with multiplication: VISUALLY

Like if you were going to use algebra tiles to look at the problem on a table, you can draw out the algebra tiles on a sheet of paper. The first step to doing this is by taking the expression and putting on the side on top of a rectangle and the other side on the right side of the rectangle. Then by lining up the shapes, you will get the simplified answer. After writing out the answer in its numeric form.

An example:

Another way to evaluate a polynomial expression: AREA MODEL

When we were learning about these in math class, it made me remember in science when we were learning about Punnett Square and how they looked and worked similarly. In an area model, you will divide up the expression into different terms. Then make a square and put the terms on the sides of the square. The two terms that meet in the middle to make another square get multiply together. In the end, you add all of the sums from the numbers.

An example: