How to Combine Like Terms

Like Terms are those terms that are containing identical variables that are raised to identical power(s).

For example, the terms −8x and 3x are “like terms” here, just like 0.5xy2 and 8xy2 are “like terms”.

The concepts of the distributive property may also help us understand one fundamental idea in algebra. This that we can add and subtract quantities such as 12x and 3x in the same way as the numbers 12 and 3.

Let’s take a look at an example and see how we can do this.

Add: 3x + 12x.

From earlier study about the distributive property and also from studying and using the commutative property, we know that x(3 + 12) is exactly the same as

3(x) + 12(x).

This: x(15)

So the answer is: 3x + 12x = 15x

So we call groups of terms which are consisting of coefficients that are multiplied by identical variables “like terms”. Look at the following table that’s showing a few different sets, or groups, of these “like terms”:

Groups of Like Terms
3x, 7x, −8x, −0.5x
−1.1y, −4y, −8y
12t, 25t, 100t, 1t
4ab, −8ab, 2ab

This lesson is very important.
The concept of “combining like terms” is often used in GED Math questions.

1. Combine like terms.

\(14x^{3} - 10x^{3}\)

Question 1 of 2

2. Combine like terms.

\(9 - 17m - m + 7\)

Question 2 of 2


Next lesson: Algebraic expressions


Last Updated on April 12, 2021.

People Also Read: