Adding and Subtracting Polynomials
A polynomial looks like this:
|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?
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:
- 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 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.
To subtract Polynomials, first reverse the sign of each term we are subtracting (in other words turn "+" into "-", and "-" into "+"), then add as usual.
Note: After subtracting 2xy from 2xy we ended up with 0, so there is no need to mention the "xy" term any more.