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.
Note: the coefficients (the numbers you multiply by, such as "5" in 5x) can be different.
Example:
| 7x | x | -2x | πx |
are all like terms because the variables are all x
Example:
| (1/3)xy2 | -2xy2 | 6xy2 | xy2/2 |
are all like terms because the variables are all xy2
Adding Polynomials
Two Steps:
- Place like terms together
- Add the like terms
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 |
| Add the like terms: | (2+3)x2 | + | (6-2)x | + | (5-1) |
= 5x2 + 4x + 4
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.
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 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.