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 just easier to write x. Imagine adding eggs:

7 eggs plus 1 egg is 8 eggs
is written 7 eggs + egg = 8 eggs

 

Example: 4x3 + 3x2 − 7 − x2 + 2

Some of the terms are like terms.

Combine like terms:

(4x3) + (3x2x2) + (2 − 7)

Then add like terms:

4x3  + 2x2 − 5