Benjamin Franklin K-8 Center, Algebra I E.O.C.
Algebra & Math Education
Arithmetics with Polynomials
Watch and complete your notes on the videos below.
Afterwards, read about using Arithmetic with Polynomials. Then, test your knowledge!
Adding and Subtracting Polynomials
A polynomial looks like this:
To add polynomials we simply add any like terms together. So, what is a like term?
Like Terms
Like Terms are terms whose variables (and their exponents such as the 2 in ) are the same.
In other words, terms that are "like" each other.
Note: the coefficients (the numbers you multiply by, such as "5" in 5x) can be different.
Example:
7x x -2x π x
are all like terms because the variables are all x
Example:
are all like terms because the variables are all
Example: These are NOT like terms because the variables and/or their exponents are different:
Adding Polynomials
Two Steps:
1. Place like terms together 2. Add the like terms
Here is an animated example:
(Note: there was no "like term" for the -7 in the other polynomial, so we didn't have to add anything to it.)
Adding in Columns
We can also add them in columns like this:
Adding Several Polynomials
We can add several polynomials together like that.
Subtracting Polynomials
To subtract Polynomials, first reverse the sign of each term we are subtracting (in other words turn "+" into "-", and "-" into "+"), then add as usual.
Like this:
Note: After subtracting 2xy from 2xy we ended up with 0, so there is no need to mention the "xy" term any more.