Combining Like Terms Lessons
A term is a constant or a variable in an expression. In the equation 12+3x+2x2=5x-1, the terms on the left are 12, 3x and 2x2, while the terms on the right are 5x, and -1.
Combining Like Terms is a process used to simplify an expression or an equation using addition and subtraction of the coefficients of terms. Consider the expression below
5 + 7
By adding 5 and 7, you can easily find that the expression is equivalent to
What Does Combining Like Terms Do?
Algebraic expressions can be simplified like the example above by Combining Like Terms. Consider the algebraic expression below:
12x + 7 + 5x
As you will soon learn, 12x and 5x are like terms. Therefore the coefficients, 12 and 5, can be added. This is a simple example of Combining Like Terms.
17x + 7
What are Like Terms?
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.
The following are like terms because each term consists of a single variable, x, and a numeric coefficient.2x, 45x, x, 0x, -26x, -xEach of the following are like terms because they are all constants.15, -2, 27, 9043, 0.6Each of the following are like terms because they are all y2 with a coefficient.3y2, y2, -y2, 26y2
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, 17zEach y variable in the terms below has a different exponent, therefore these are unlike terms.15y, 19y2, 31y5Although both terms below have an x variable, only one term has the y variable, thus these are not like terms either.19x, 14xy
The next page will walk you through the process of combining like terms in a simple equation.