Like terms

In algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match.

Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power. For example, 8xyz² and −5xyz² are like terms because they have the same variables and power while 3abc and 3ghi are unlike terms because they have different variables. Since the coefficient doesn't affect likeness, all constant terms are like terms.

In this discussion, a "term" will refer to a string of numbers being multiplied or divided (remember that division is simply multiplication by a reciprocal) together. Terms are within the same expression and are combined by either addition or subtraction. For example, take the expression:

${\displaystyle ax+bx\,\!}$

There are two terms in this expression. Notice that the two terms have a common factor, that is, both terms have an ${\displaystyle x\,\!}$. This means that we can factor out that common factor variable, resulting in

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