Adding and Subtracting Polynomials

A polynomial looks like this:

polynomial example
example of a polynomial
this one has 3 terms

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 x2) 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.



are all like terms because the variables are all x



are all like terms because the variables are all xy2

Example: These are NOT like terms because the variables and/or their exponents are different:


Adding Polynomials

Two Steps:

Example: Add   2x2 + 6x + 5   and   3x2 - 2x - 1

Start with:2x2 + 6x + 5   +   3x2 − 2x − 1
Place like terms together:2x2+3x2   +   6x−2x   +   5−1
Which is:(2+3)x2  +   (6−2)x   +   (5−1)
Add the like terms:5x2  +   4x   +   4

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.

Example: Add    (2x2 + 6y + 3xy)  ,   (3x2 - 5xy - x)   and   (6xy + 5)

Line them up in columns and add:

2x2 + 6y + 3xy
3x2      - 5xy - x
           6xy     + 5
5x2 + 6y + 4xy - x + 5

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

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.


344, 345, 3186, 3187, 3883, 3884, 1098, 2094, 1099, 2095