Combining like terms is adding or subtracting algebraic terms that have the same variable and exponent. In Elementary Algebra, it is a core simplification move before solving equations.
Combining like terms is the algebra step where you add or subtract terms that match exactly in their variable part. In Elementary Algebra, that means the terms must have the same variable and the same exponent. For example, 3x and -5x are like terms, but 3x and 3x^2 are not.
The reason this works is that you are only changing the coefficients, the numbers in front of the variables. The variable part stays the same. So 7y - 2y becomes 5y, and 4a + 9a - 3a becomes 10a. You are not changing what the variable stands for, just how many of that same kind you have.
This is different from combining unlike terms. You cannot turn x and y into xy, and you cannot combine x with x^2. Those terms are different because the exponent changes the meaning of the term. A good shortcut is to ask, “Do these terms have the exact same variable part?” If the answer is yes, you can combine them. If not, leave them separate.
You will often combine like terms after simplifying inside parentheses or distributing a number across an expression. That makes the expression shorter and easier to work with. For instance, in 2(3x + 4) + 5x, you would first distribute to get 6x + 8 + 5x, then combine the like terms 6x and 5x to get 11x + 8.
A common mistake is adding the exponents instead of the coefficients. For example, x + x is 2x, not x^2. The exponent only matters when deciding whether terms match. Once the terms are like terms, you combine the numbers attached to them, not the variable itself.
Combining like terms is one of the main cleanup steps in Elementary Algebra because it turns messy expressions into ones you can actually solve. If an equation has several x terms on one side, combining them first makes it much easier to isolate the variable and follow a clear solving strategy.
It also shows up in nearly every unit that builds on expressions and equations. When you simplify a polynomial, reduce a word problem into an algebraic expression, or check whether two expressions are equivalent, you usually need to combine like terms somewhere in the process.
This skill connects directly to solving linear equations. For example, if you have 4x + 3x - 2 = 19, combining like terms gives 7x - 2 = 19. That smaller equation is easier to solve with inverse operations than the original version.
It also trains you to read algebra carefully. The variable part tells you what can be combined, and the coefficient tells you how much you have. Once you can separate those pieces quickly, a lot of Elementary Algebra starts to feel more manageable.
Keep studying Elementary Algebra Unit 2
Visual cheatsheet
view galleryCoefficient
The coefficient is the number attached to a variable, and that is the part you actually add or subtract when combining like terms. In 8x - 3x, the variable part stays x, while the coefficients 8 and -3 combine to make 5. If you confuse the coefficient with the variable part, the whole simplification breaks down.
Variable
Terms can only be combined when they have the same variable part. That means x and y are not like terms, even if both have a coefficient of 1. Knowing what the variable stands for helps you spot which terms match and which terms need to stay separate.
Exponent
The exponent tells you how many times a variable is used as a factor, so it changes whether terms are alike. x and x^2 are not like terms because the exponent is different. In Elementary Algebra, checking the exponent is just as important as checking the letter itself.
Inverse Operations
After you combine like terms, inverse operations are usually the next move when solving equations. Simplifying first makes those steps cleaner because you have fewer pieces to undo. For example, 3x + 2x = 5x before you subtract, divide, or add to isolate the variable.
A quiz or problem set question will usually give you an expression like 5x + 2 + 3x - 7 and ask you to simplify it. Your job is to sort the like terms, combine the x terms, and leave the constant terms alone. If the expression has parentheses first, you may need to distribute before combining. A strong answer shows that you know why 5x and 3x combine, but 2 and -7 combine separately. If the expression is part of an equation, combining like terms often comes before inverse operations so you can isolate the variable more easily.
Distributing and combining like terms are different steps. Distributing breaks apart a factor outside parentheses, like 2(x + 3) becoming 2x + 6. Combining like terms comes after that, when you simplify terms that already have matching variables and exponents. Students often mix them up because both can happen in the same problem.
Combining like terms means adding or subtracting only the coefficients of terms with the same variable part and the same exponent.
x and x are like terms, but x and x^2 are not, because the exponent changes the term.
You can combine constants with constants too, since they have no variable part.
This step makes expressions shorter and makes equations easier to solve with inverse operations.
If terms do not match exactly, leave them separate instead of forcing them together.
It is the process of adding or subtracting terms that have the same variable and exponent. For example, 4x + 7x becomes 11x, and 6 - 2 becomes 4. You keep the variable part the same and only combine the coefficients.
Ask whether the variable part matches exactly, including the exponent. 3a and -8a are like terms, but 3a and 3a^2 are not. Different variables also make terms unlike, so x and y cannot be combined.
No. Exponents are not added when you combine like terms. You only add or subtract the coefficients. That is why x + x = 2x, not x^2.
Combining like terms reduces the number of pieces in the equation, which makes isolating the variable easier. For example, 2x + 5x - 4 = 17 becomes 7x - 4 = 17. From there, inverse operations are simpler to apply.