Learning How to Multiply Polynomials Together

When it comes to multiplying polynomials, a lot of people get stuck and aren’t really sure what to do. This normally happens because people get anxious over the amount of information they’re having to deal with and try to hold it all in their memory at once. This isn’t the right way to handle things because it takes away from the actual multiplication process and makes it hard to focus on what you’re doing.

2x^3y^4 * 5x^6y^2

Before you can multiply whole polynomials, you have to be able to quickly and intuitively multiply polynomial terms. All this involves is using the commutative property of multiplication to rearrange the order of the variables and constants in question. For example, if we have, then we can drop all of the parenthesis to really have just, and we can rearrange the order however we want. To make things easy on ourselves, we should put the constants beside of each other and all similar variables beside each other to get something like which simplifies to just give us. Notice that the exponents for each variable just add together.

(a + b + c)(d + e + f)
(a + b + c)
(d + e + f)

Once you have the idea of multiplying polynomials terms down pat, you can move on to multiplying whole polynomials, which requires the application of the distributive property. Let’s use some simple polynomials like for an example. First we’ll distribute to each of the terms of, and then do the indicated distributions that come up from there and simplify as much as we can. Here’s what it could look like:

(a + b + c)(d + e + f)
ad + bd + cd + ae + be + ce + af + bf + cf

There’s not really much to multiplying polynomials as long as you stay focused on the process at hand instead of trying to remember the exact form of all of the polynomials you’re dealing with. They’re written down in front of you for a reason! You will not forget them.