Combining like terms is adding or subtracting terms with the same variable part and exponent, such as 3x and 5x. In Intermediate Algebra, it is one of the first simplification steps before solving equations.
Combining like terms is the step where you simplify an algebraic expression by grouping terms with the same variable part and adding their coefficients. In Intermediate Algebra, that means terms like 4x and 9x can combine, but 4x and 4x^2 cannot, because the exponent changes the term.
The idea is really about the variable part staying identical. If two terms both have x, or both have x^2, or both have ab, they may be like terms. The numbers in front of them are the coefficients, and those are what you add or subtract. So 7x - 2x becomes 5x, and 3a + 8a - a becomes 10a.
You do not combine terms just because they look similar at a glance. A term with a variable is not the same as a constant, so 6x + 4 stays as two terms. Also, x and y are different variables, so 5x + 5y does not simplify further. In an expression with several pieces, you often rearrange terms first so the matching ones sit together.
This is why combining like terms shows up right before or during solving equations. If an equation has 2x + 5x - 3 = 18, you simplify the left side to 7x - 3 before isolating x. That makes the problem easier to see and keeps the algebra from getting messy.
A helpful way to check yourself is to ask, “Do the variable parts match exactly?” If yes, combine the coefficients. If no, leave the terms separate. That check saves a lot of mistakes when expressions include negatives, multiple variables, or powers.
Combining like terms is one of the main cleanup moves in Intermediate Algebra. Without it, expressions stay cluttered, and later steps like using the distributive property, clearing fractions, or solving linear equations get harder to follow.
It also builds the habit of reading algebra structurally instead of symbol by symbol. You start seeing that 3x, -x, and 10x are all the same type of term, while 3x and 3x^2 are not. That distinction shows up again when you work with polynomials, rational expressions, and systems of equations.
In linear equations, combining like terms is often the first simplification step before you move variables to one side with the Addition Property of Equality. If you skip it, you may still reach the right answer, but the work is longer and the chance of error goes up.
It also connects to equivalent expressions. When you combine like terms correctly, you are not changing the value of the expression, just rewriting it in a shorter form. That skill matters every time you simplify an expression before graphing, factoring, or checking a solution.
Keep studying Intermediate Algebra Unit 2
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When you combine like terms, you add or subtract the coefficients, not the variable itself. In 4x + 7x, the coefficients are 4 and 7, and the result is 11x. If a term looks like -x, that coefficient is really -1, which matters when you simplify negative terms.
Variable
Like terms must have the same variable part. That means x and y do not combine, and x also does not combine with x^2. Seeing the variable clearly helps you decide whether terms belong together or should stay separate.
Distributive Property
The distributive property often creates expressions that need combining like terms afterward. For example, 2(x + 3) becomes 2x + 6, and then you may combine that with other x terms or constants. In Intermediate Algebra, these two moves often work together.
Equivalent Equations
Combining like terms does not change the meaning of an equation when you do it correctly on one side or both sides. You are rewriting the expression in a simpler form, which keeps the equation equivalent. That makes it easier to isolate the variable without changing the solution.
A quiz problem will usually ask you to simplify an expression or clean up one side of an equation before solving. Your job is to sort the terms by variable part, combine the matching ones, and leave unlike terms alone. For example, 6x + 2 - 3x + 5 becomes 3x + 7, not 9x or 11x.
If the problem includes parentheses, you may need to use the distributive property first, then combine like terms. Watch negatives carefully, because a subtraction sign in front of a term changes the coefficient. Teachers also like to check whether you know that x and x^2 are different terms, since that mistake shows up a lot in unit tests and homework sets.
Combining like terms and the distributive property are different steps. The distributive property removes parentheses by multiplying, while combining like terms simplifies what is left by adding or subtracting matching terms. A lot of problems use both, but they are not the same move.
Combining like terms means adding or subtracting terms with the same variable part and the same exponent.
You only combine the coefficients, so 4x + 9x becomes 13x, not 36x.
Terms like x and x^2 are not like terms, and x and y are not like terms either.
This step usually comes before solving equations because it makes the expression shorter and easier to work with.
Negative signs matter, so a term like -x counts as -1x when you combine it.
It is the process of simplifying an expression by adding or subtracting the coefficients of terms that have the same variable part. For example, 5x + 2x becomes 7x, and 3y - y becomes 2y. The variable part has to match exactly for the terms to combine.
The variable part must be identical, including the exponent. So 4a and -9a are like terms, but 4a and 4a^2 are not. Constants can combine with constants, and terms with different variables stay separate.
You combine the coefficients. The variable part stays the same, and only the numbers in front of the variable get added or subtracted. For example, in 8x - 3x, you do 8 - 3 and keep the x, giving 5x.
Yes, and that is very common in Intermediate Algebra. First you clear the parentheses, then you combine any like terms that appear. A problem like 2(x + 4) + 3x becomes 2x + 8 + 3x, then 5x + 8.