Combining Like Terms
From Teach And Discover Wiki
Combining Like Terms is a process used to simplify an expression or an equation using addition and subtraction of the coefficients of terms. In case you didn't know, a term is each single part of an expression. For example, in the expression 4x + 3 + 7y, there are three terms: 4x, 3, and 7y. The number 4 is not a term, but rather a factor of the term 4x. Each term is separated by a plus sign (+) or a minus sign (-). The key to using and understanding the method of Combining Like Terms is to understand like terms and be able to identify when a pair of terms is a pair of like terms. Some examples of like terms are presented below.
Like Terms
The following are like terms because each term consists of a single variable, x, and a numeric coefficient.
- 2x, 45x, x, 0x, -26x, -x
Each of the following are like terms because they are all constants.
- 15, -2, 27, 9043, 0.6
Each of the following are like terms because they are all y2 with a coefficient.
- 3y2, y2, -y2, 26y2
Unlike Terms
For comparison, below are a few examples of unlike terms.
The following two terms both have a single variable with an exponent of 1, but the terms are not alike since different variables are used.
- 17x, 17z
Each y variable in the terms below has a different exponent, therefore these are unlike terms.
- 15y, 19y2, 31y5
Although both terms below have an x variable, only one term has the y variable, thus these are not like terms either.
- 19x, 14xy
