##### 6.6 Multiplying polynomial by polynomial

Previously, we discussed Polynomials and Multiplication and division of polynomials. From there we learned that Polynomials are expressions that contain terms which are comprised of the combination of a coefficient, a constant, variables and exponents. We also learned that it can come in different forms depending on the number of terms that the expression has, monomial for one term, binomial for two terms, trinomial for three terms and polynomial for more than three terms.

These terms can be combined through the four different operations namely addition, subtraction, multiplication and division with the exemption of division wherein the denominator is a variable. In this chapter we will focus a bit more in multiplying polynomials, particularly monomial by monomials, monomials by binomials, binomial by binomial and polynomial by polynomial.

Apart from the terms there are also other components of a polynomial. In previous chapter, we learned that each term of the polynomial has a degree, and it is denoted by its exponent. We also learned that the highest degree of the polynomial indicates the degree of the polynomial. So if you’re given the term 5x, you will know that it’s degree is 1. If you’re given the expression $5x^3 + 2x^2$, the degree of each terms are, 3, and 2 respectively, and the degree of the polynomial is 3.

We will also look into the application of polynomials in solving for problems in geometry especially that of finding the area of shaded regions and non shaded regions. To illustrate this application you can try graphing polynomial expressions with a free polynomial graphing tool online.

### Multiplying polynomial by polynomial

When multiplying polynomials, we need to distribute each term in the first polynomial to every term in the second polynomial. Then, we combine any like terms.