Unit 5.3 Polynomials Multiplication
Multiplication
To multiply a polynomial, it is not as simple as multiplying the like terms together. There are a few different ways to multiply polynomials. One method is the box method and the other is the FOIL method. FOIL stands for First, Outer, Inner Last. This is the order that you multiply the terms together to ensure that all terms are accounted for.
For the binomials (x + 2) (x + 4)
Method 1: FOIL Method
Multiply the first terms in each parenthesis together
Multiply the outmost terms of the two binomials
Multiply the two most inner terms of the two binomials
Lastly, multiply the last two terms of each binomial
Combine all the multiplied terms into one polynomial and combine like terms
Method 2: Box Method
Set up a grid with the values from one binomial on top and the second one on the left hand side. Be sure to include if the values are negative. In this case since we are multiplying a binomial (2 terms) by a binomial (2 terms) the grid is a 2×2
Multiply the values together by taking the value that is on the left side and the top
Simplify
Write out each term into a single polynomial and simplify
The Box method can be used for a variety of polynomial multiplication problems. If you wanted to multiply a trinomial by a trinomial for example, the setup would look like this:
