Combining like terms is simplifying an expression by adding or subtracting the terms that have exactly the same variable part. You add their coefficients and keep the variable part: 3x + 2x = 5x. Constants combine with constants. So 3x + 5 + 2x − 1 simplifies to 5x + 4.
In Spanish
combinar términos semejantes
Also called
collecting like terms, simplifying an expression, adding like terms
Like terms are the same kind of tile. Put the x-tiles together and the unit tiles together: 3x + 2x = 5x and 5 − 1 = 4, so the expression is 5x + 4.
Formal definition and notation
Two terms are like terms when they contain the same variables raised to the same powers, such as 4ab2 and −ab2. Combining them uses the distributive property in reverse: axm + bxm = (a + b)xm. The result is an equivalent expression with fewer terms, equal to the original for every value of the variables.
Symbol
Read it as
Meaning
ax + bx = (a + b)x
a x plus b x equals a plus b, times x
the rule behind combining like terms
x = 1x
x equals one x
a term with no written coefficient has coefficient 1
−x = −1x
negative x equals negative one x
a lone minus sign means coefficient −1
Key facts
Only like terms combine: 3x and −7x are like terms; 3x and 3x2 are not; 5 and −2 are like terms (both constants).
The sign in front of a term belongs to it: in 8 − 3y + y, the terms are 8, −3y and +y, so −3y + y = −2y.
Combining like terms never changes the exponents: 2x2 + 3x2 = 5x2, not 5x4.
It is the first step in solving many equations: 4x + 7 − x = 22 becomes 3x + 7 = 22.
Steps for combining like terms
Steps for combining like terms
axn + bxn = (a + b)xn
a, b
the coefficients, which you add or subtract
xn
the shared variable part, which stays exactly the same
(1) Distribute to clear parentheses. (2) Mark each term with its sign in front of it. (3) Group like terms. (4) Add their coefficients. (5) Write the answer, usually from the highest power down.
Group the a-terms and the constants: (7a − 2a) + (3 + 9).
Combine the a-terms: 7 − 2 = 5, so 5a.
Combine the constants: 3 + 9 = 12.
Answer:7a + 3 − 2a + 9 = 5a + 12.
Example 2: Squared terms and negatives
Core
Simplify 4x2 − 3x + 6 − x2 + 8x − 10.
x2-terms: 4x2 − x2 = 3x2 (the lone −x2 has coefficient −1).
x-terms: −3x + 8x = 5x.
Constants: 6 − 10 = −4.
Write from the highest power down: 3x2 + 5x − 4.
Answer: The expression simplifies to 3x2 + 5x − 4.
Example 3: Distribute first, then combine
Test-style
Which expression is equivalent to 3(2y − 5) − 4(y − 2)?
Distribute the 3: 6y − 15.
Distribute the −4 to both terms: −4y + 8.
Combine y-terms: 6y − 4y = 2y.
Combine constants: −15 + 8 = −7.
Answer:3(2y − 5) − 4(y − 2) = 2y − 7.
Common mistakes
✗ Mistake4x + 3 = 7x.
✓ Instead4x + 3 is already simplified: the terms are not alike.
A term with x and a constant are different kinds of quantities, like 4 apples and 3 dollars. Only terms with the same variable part combine.
✗ Mistake5x2 + 2x2 = 7x4.
✓ Instead5x2 + 2x2 = 7x2.
When you add like terms, you add the coefficients only. The variable part, including its exponent, stays the same. Exponents add when you multiply, not when you add.
✗ Mistake9 − 4(y − 2) = 9 − 4y − 8 = 1 − 4y.
✓ Instead9 − 4(y − 2) = 9 − 4y + 8 = 17 − 4y.
The −4 multiplies both terms in the parentheses, and −4 × (−2) = +8.
✗ Mistake6m − m = 6.
✓ Instead6m − m = 6m − 1m = 5m.
A variable with no number in front has coefficient 1. Taking away one m from six m leaves five m.
Combining like terms rewrites an expression, such as 2x + 3x = 5x, without finding x. Solving an equation such as 5x = 20 finds the value x = 4.
Quick check: 3 questions
Question 1 of 3
Simplify 8n − 3 + 2n + 10.
Show answer and explanation
Answer: B.8n + 2n = 10n and −3 + 10 = 7, so 10n + 7. 17n wrongly combines numbers with n-terms, 6n + 7 subtracts the n-terms, and 10n − 13 mishandles the signs of the constants.
Question 2 of 3
Which pair are like terms?
Show answer and explanation
Answer: D.pq and qp are the same variable part, because multiplication can be done in any order. The other pairs differ in a variable or an exponent, even when the coefficients match.
Question 3 of 3
Simplify 5(x + 1) − 2x.
Show answer and explanation
Answer: A. Distribute: 5x + 5 − 2x. Combine: 3x + 5. 3x + 1 forgets to distribute to the 1, 7x + 5 adds instead of subtracting, and 8x combines unlike terms.
Combining Like Terms: frequently asked questions
How do you combine like terms?
First clear any parentheses with the distributive property. Then find the terms whose variable parts match exactly, including exponents, and keep the sign in front of each term with it. Add or subtract their coefficients and keep the variable part. For 2x + 7 − 5x + 1, that gives −3x + 8.
Can you combine x and x squared?
No. x and x2 are different kinds of terms, so 4x2 + 3x cannot be simplified further. Try x = 2: 4x2 + 3x = 16 + 6 = 22, but 7x3 would give 56, so they are not the same. Only terms with the same variables and the same exponents can be combined.
Why does combining like terms work?
It is the distributive property used backward. 3x + 2x means three x‘s plus two x‘s, and 3x + 2x = (3 + 2)x = 5x. Because each step uses a property of numbers, the simplified expression gives the same value as the original for every value of x.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 6.EE.A.3, CCSS 6.EE.A.4, CCSS 7.EE.A.1
Cite this entry
Effortless Math Team. “Combining Like Terms.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/combining-like-terms/
Flashcard
TermCombining Like Terms3x + 5 + 2x − 1
DefinitionAdd the coefficients of terms with the same variable part, and combine the constants: 3x + 5 + 2x − 1 = 5x + 4.
ExpressionAn expression is a number, variable, or combination of numbers and variables joined by operations, without an equal sign. Examples are 7, 4x + 9 and 3(a − 2). Expressions can be simplified, but they are not solved unless they are part of an equation. You evaluate one by replacing each variable with a number.Algebra · Grade 6, Grade 7, Grade 8CoefficientA coefficient is the number multiplied by a variable in a term. In 4a the coefficient is 4, in −3x it is −3, and in x it is 1, because x = 1x. The sign in front belongs to the coefficient. A number standing alone, with no variable, is a constant instead.Algebra · Grade 6, Grade 7, Grade 8Like TermsLike terms have exactly the same variables raised to exactly the same powers; only their coefficients may differ. 3x and 8x are like terms, and so are 5a2 and −2a2, but 4x and 4y are not. Only like terms can be combined by adding or subtracting their coefficients: 3x + 8x = 11x.Algebra · Grade 6, Grade 7, Grade 8VariableA variable is a letter or symbol that represents a number or value, usually one that can change or is not yet known. In n + 5 = 12, the variable n is an unknown that equals 7. In A = lw, the variables l and w can take many values. Any letter can be a variable, not just x.Algebra · Grade 6, Grade 7, Grade 8PowerA power is a number written as a base with an exponent, such as 53, or the value that results, 53 = 5 × 5 × 5 = 125. We say 125 is the third power of 5, or “5 to the third power”. The second power is called the square and the third power the cube.Number System · Grade 5, Grade 6, Grade 7Distributive PropertyThe distributive property says that multiplying a number by a sum gives the same result as multiplying it by each term and then adding: a(b + c) = ab + ac. It multiplies a factor by each term inside parentheses, so 3(x + 4) = 3x + 12. It works with subtraction too, and using it backward is factoring.Algebra · Grade 6, Grade 7, Grade 8Equivalent ExpressionsEquivalent expressions are expressions that have the same value for every value of the variable, even though they look different. For example, 3(x + 2) and 3x + 6 are equivalent: both equal 15 when x = 3 and 0 when x = −2. You build them with the properties of operations, such as the distributive property.Algebra · Grade 6, Grade 7, Algebra 1Equal ToEqual to means having exactly the same value or amount, and it is written with the symbol =. Numbers that look different can still be equal to each other: 12 is equal to 0.5. When two amounts are not the same, one is greater than or less than the other.Symbols and Notation · Kindergarten, Grade 1, Grade 2ExponentAn exponent tells how many times to use a base as a factor. It is the small raised number to the upper right of the base: in 53, the base is 5 and the exponent is 3, so 53 = 5 × 5 × 5 = 125. Any nonzero number with an exponent of 0 equals 1.Algebra · Grade 6, Grade 7, Grade 8Commutative PropertyThe commutative property says that changing the order of the numbers does not change the result of adding or multiplying them: a + b = b + a and a × b = b × a. For example, 4 + 9 = 9 + 4 and 3 × 5 = 5 × 3. Subtraction and division are not commutative.Operations · Grade 1, Grade 3, Grade 6SimplifySimplify means to rewrite a number or expression in a shorter, easier form without changing its value. To simplify a fraction, divide the numerator and denominator by a common factor until none is left: 1824 = 34. To simplify an expression, combine like terms and do the operations you can: 3x + 2x = 5x.Number System · Grade 4, Grade 5, Grade 6NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2EquationAn equation is a statement that two expressions are equal. It always has an equal sign, such as x + 5 = 12 or 3a = 18. Solving an equation means finding the value of the variable that makes it true: here x = 7 and a = 6. An expression like 4x + 7 has no equal sign, so it is not an equation.Algebra · Grade 6, Grade 7, Grade 8PolynomialA polynomial is an expression built from variables and coefficients using only addition, subtraction, and multiplication, with whole-number exponents. Examples are 3x2 + 5x − 7 and x + 9. Its degree is the highest exponent it contains. A variable in a denominator or under a square root usually means the expression is not a polynomial.Algebra · Algebra 1, Algebra 2MonomialA monomial is a single term made of a number, a variable, or a product of numbers and variables with whole-number exponents, such as 8, x, or −7x2y. It has no addition or subtraction, and no variable in a denominator. Its degree is the sum of the exponents on its variables.Algebra · Grade 8, Algebra 1Order of OperationsThe order of operations is the agreed sequence for evaluating an expression: parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. Without it the same expression would have several answers. Many students remember it as PEMDAS.Algebra · Grade 5, Grade 6, Grade 7TermA term is a single number, a variable, or numbers and variables multiplied together, such as 7, x or −4xy2. In an expression, terms are the parts separated by plus and minus signs, so 5x2 − 3x + 8 has three terms. The sign in front of a term belongs to it.Algebra · Grade 6, Grade 7, Algebra 1