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Like Terms

TOPIC OVERVIEW
In this article, I will explain the use of a Like Term, and suggest a better way of thinking about the topic. Please add your ideas in the comments.

Like Term: This is a term whose variables 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

    (1/3)xy2
    −2xy2
    6xy2
    xy2/2
    Are all like terms because the variables are all x
    Unlike Term: If they are not like terms, they are called "Unlike Terms":

    Unlike Terms
    Why they are "Unlike Terms"
    −2xy
    −4y
    13y2
    ← these are all unlike terms 
    ( xy, y and y2 are all different)

    2x      2x2     2y      2xy
    These are all Unlike Terms because the variables and/or their exponents are different.

    COMBINING OF LIKE TERMS

    You can add Like Terms together to make one term:

    Example:

    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:
    5 eggs plus 1 egg is 6 eggs
    is written 5 eggs + egg = 6 eggs
    You can subtract Like Terms:

    Example:

    They are both like terms, so you can just subtract them:
    3y - 2y = y
    Note: these are Like Term by y
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