Image used by permission of the original author, Chris Burke.

How to Combine Like Terms

Rules for Combing Like Terms

What are 'like terms' ?

Like terms are two things that can be added.

In more technical speak, like terms have the same variables and the same exponents.

Like terms are two things that can added.

"Like Terms" means that you can add or subtract two terms. For instance, you know that you can add $$2 + 3$$ and get 5. You were able to add these two 'terms' ( the '2' and the '3') because they are both numbers! However, you might also know that you cannot 'combine' 2 and x. Since 2 is a number and 'x' is not, they are not like terms.

Examples

Examples of Like Terms Examples that are NOT like Terms
$$3 + 2$$ $$3 + x$$
$$x + 2x$$ $$x + 2$$
$$3x + 5x$$ $$3x^2 + 5x$$
$$x^2 + 3x^2$$ $$x^2 + 3x^3$$
$$2x^{21} + 3x^{21}$$ $$2x^{23} + 3x^{21}$$
$$2x^{a} + 3x^{a}$$ $$2x^{a} + 3x^{ab}$$ ($$b \ne 1$$)

Video on how to combine Like Terms

• Exponents and Bases: You may have noticed that like terms always have the same base and exponent.
• Regarding Coefficients: Also, the coefficient in front of a variable does not change whether or not terms are alike. For instance 3x and 5x and 11x are all like terms. The coefficients ( the '3' in 3x, '5' in 5x and '11' in 11x) do not have anything at all to do with whether or not the terms are like. All that matters is that each of 'x' factors or 'bases' have the same exponent.

Practice Combining Like Terms

Problem 1
x and 2x are like terms so you combine, or add, them to become 3x. Therefore the final answer is 3x + 2
Problem 2
5 and 2 are like terms so you can combine them to become 7. Therefore the final answer is 7 + x
Problem 3
3x and 2x are like terms (Remember the coefficients do not matter) so you can combine (ie 'add') them to become 5x. The final answer is 5x + 6
Problem 4

2x and x are like terms so you can combine (ie 'add') them to become 3x. Likewise, 3 and 6 are like terms and can be added to 9. The final answer is 3x + 9

More Challenging problems

Problem 5

2x2 and x2 are like terms so you can combine (ie 'add') them to become 3x2. Likewise, 13 and 6 are like terms and can be added to 19. The final answer is 3x2 + 19

Problem 6

2x3 and 4x3 are the only like terms --combine (ie 'add') them to become 6x3. Likewise, 13 and 6 are like terms and can be added to 19. The final answer is 6x3 + x2 + 3x