Like Terms
It may help you to read Introduction to Algebra first
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
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
Unlike Terms
If they are not like terms, they are called "Unlike Terms":
| Unlike Terms | Why they are "Unlike Terms" | ||
|---|---|---|---|
| −3xy | −3y | 12y2 | ← these are all unlike terms (xy, y and y2 are all different) |
Example: These are all Unlike Terms because the variables and/or their exponents are different:
2x
2x2
2y
2xy
Combining Like Terms
You can add like terms together to make one term:
Example: 7x + x
They are both like terms, so you can just add them:
7x + x = 8x
By the way ... why don't we write "1x" ?
It is simpler to write x, and is so common that "1x" looks strange.
Example: 4x3 + 3x2 − 7 − x2 + 2
Some of the terms are like terms.
Combine like terms:
(4x3) + (3x2 − x2) + (2 − 7)
Then add like terms:
4x3 + 2x2 − 5