Adding and Subtracting Polynomials

A polynomial looks like this:

example of a polynomial this one has 3 terms

To add polynomials you 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 x²) are the same.

In other words, terms that are "like" each other.

Examples:

Terms				Why are they "Like Terms"
	7x	x	-2x	because the variables are all x
	(1/3)xy2	-2xy2	6xy2	because the variables are all xy2

Adding the Polynomials

Two Steps:

• Place like terms together
• Add the like terms

Here is an animation to show you:

(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

You could also add them in columns like this:

Adding Several Polynomials

You can add several polynomials together like that.

Using columns helps you to match the correct terms together in a complicated sum.

Subtracting Polynomials

To subtract Polynomials, first reverse the sign of each term you 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.