What Are Like Terms in Algebra? Definition, Examples & How to Combine Them

Introduction

Take a look at this simple expression: 3x + 5x

Both terms contain exactly the same variable, x, raised to exactly the same power. Because of that, they can be added together to give 8x. The terms 3x and 5x are called like terms.

So, what are like terms in algebra? Like terms are algebraic terms that have exactly the same variable or variables, each raised to exactly the same power. The numerical coefficients in front of those variables can be completely different. What matters is that the variable parts are identical.

Understanding like terms is one of the most important foundational skills in algebra. It allows you to simplify expressions, solve equations more efficiently, and lay the groundwork for every topic that comes after it in mathematics.

Key Takeaways

• Like terms share exactly the same variables raised to exactly the same exponents.

• The numerical coefficients do not need to be equal for two terms to be like terms.

• Like terms can be combined by adding or subtracting their coefficients.

• Unlike terms have different variables or different exponents and cannot normally be combined.

• Constants such as 5 and -3 are always like terms because neither contains a variable.

• Combining like terms is the main method used to simplify algebraic expressions.

• Multi-variable terms such as 3xy and 7xy are like terms because their entire variable parts match.

What Are Like Terms in Algebra?

Like terms are algebraic terms that have identical variable parts. Two conditions must both be true for terms to be like terms:

1. They must contain exactly the same variables.
2. Each of those variables must be raised to exactly the same exponent.

The numerical coefficient in front of the variable part does not matter when deciding whether two terms are like. It is the variable part only that determines this.

Here are clear examples:

• 3x and 7x — Both have the variable x raised to the power of 1. They are like terms.
• 5a² and -2a² — Both have the variable a raised to the power of 2. They are like terms.
• 4xy and 9xy — Both have exactly the same variables x and y, each to the power of 1. They are like terms.

In every case, the coefficient is different, but the variable part is identical. That is the defining feature of like terms.

Simple Examples of Like Terms

The following table shows fifteen pairs of like terms, with a brief explanation of why each pair qualifies:

Each pair has identical variable parts. That is the only requirement, regardless of how different the coefficients are.

What Are Unlike Terms?

Unlike terms are terms that do not have identical variable parts. They cannot be simplified into a single term by addition or subtraction.

Examples of unlike terms:

• 3x and 4y — Different variables (x versus y).
• x and x² — Same variable but different exponents (1 versus 2).
• 2a² and 2a³ — Same variable but different exponents (2 versus 3).
• 5xy and 5x — First term has both x and y; second has only x.
• 4 and 4x — One is a constant; the other contains a variable.
• 3x²y and 3xy² — The exponents on x and y are in different positions.

You simply cannot add or subtract unlike terms into a single term because they represent mathematically different quantities. Adding 3x and 4y together does not simplify to 7 of anything, because x and y may represent completely different values.

Like Terms vs Unlike Terms

How to Identify Like Terms

Follow this simple process every time:

1. Look at the first term. Write down its variable part, ignoring the coefficient.
2. Look at the second term. Write down its variable part, ignoring the coefficient.
3. Compare the variable parts exactly. Both the variables and their exponents must be the same.
4. Ignore the coefficients completely when checking whether terms are like.
5. If the variable parts match exactly, the terms are like terms.

Example 1: Are 4x² and -7x² like terms?
Variable part of 4x² = x²
Variable part of -7x² = x²
They match. Yes, they are like terms.

Example 2: Are 3xy and 3x²y like terms?
Variable part of 3xy = xy
Variable part of 3x²y = x²y
They do not match (the exponent on x differs). No, they are unlike terms.

Example 3: Are 6mn² and -mn² like terms?
Variable part of 6mn² = mn²
Variable part of -mn² = mn²
They match. Yes, they are like terms.

Example 4: Are 8 and -2 like terms?
Both are constants with no variable part. Constants always match. Yes, they are like terms.

Why Do Like Terms Have to Match?

Think of variables as representing units. If x represents apples, then 3x means three apples and 5x means five apples. Adding them together gives 8x, or eight apples. That makes perfect sense.

Now suppose y represents oranges. Saying 3x + 5y gives you three apples and five oranges. You cannot combine these into a single quantity of one type of fruit. They are different things entirely.

In exactly the same way, 3x and 5x represent the same type of algebraic quantity, so they can be combined:

3x + 5x = 8x

But 3x and 5y represent different algebraic quantities. They cannot combine into a single term:

3x + 5y remains as 3x + 5y

The mathematics of algebra requires that terms represent the same base quantity before they can be added or subtracted. That is precisely what the matching variable parts guarantee.

How to Combine Like Terms

The rule is simple: add or subtract the coefficients while keeping the variable part unchanged.

The variable part never changes. Only the number in front of it changes.

Examples:

3x + 5x = (3 + 5)x = 8x

7a – 2a = (7 – 2)a = 5a

4x² + 6x² = (4 + 6)x² = 10x²

Think of it as arithmetic on the coefficients. The variable part is simply carried along unchanged.

Combining Like Terms With Positive Numbers

Example 1: 4x + 3x
Coefficients: 4 + 3 = 7
Result: 7x

Example 2: 2a + 9a + a
Coefficients: 2 + 9 + 1 = 12
Result: 12a

Example 3: 5y² + 3y² + y²
Coefficients: 5 + 3 + 1 = 9
Result: 9y²

Example 4: 6mn + 4mn
Coefficients: 6 + 4 = 10
Result: 10mn

Example 5: 3 + 7 + 2 (constants)
All constants are like terms.
Result: 12

Combining Like Terms With Negative Numbers

Negative signs belong to the term immediately following them. Always keep the sign attached to the coefficient.

Example 1: 5x – 8x
Coefficients: 5 – 8 = -3
Result: -3x

Example 2: -2a + 7a
Coefficients: -2 + 7 = 5
Result: 5a

Example 3: -4x² – 3x²
Coefficients: -4 + (-3) = -7
Result: -7x²

Example 4: 9y – 4y – 2y
Coefficients: 9 – 4 – 2 = 3
Result: 3y

Example 5: -5ab + 2ab – ab
Coefficients: -5 + 2 – 1 = -4
Result: -4ab

The negative sign is a part of the coefficient. Losing it is one of the most common errors students make, so always carry the sign with the number.

Combining Like Terms With Multiple Variables

When an expression contains several different types of terms, group the like terms together first, then combine each group separately.

Example: 3x + 2y + 5x – y

Step 1: Group the x terms together.
3x + 5x = 8x

Step 2: Group the y terms together.
2y – y = y

Step 3: Write the final simplified expression.
8x + y

Another example: 7a – 3b + 2a + 5b – a

Group a terms: 7a + 2a – a = 8a
Group b terms: -3b + 5b = 2b
Result: 8a + 2b

You can rearrange the terms in any order to bring like terms together, as long as you keep their signs attached correctly.

Combining Like Terms With Exponents

When terms have exponents, the exponents must match exactly before you can combine the terms.

These can be combined:
3x² + 5x²
Both have x to the power of 2.
Result: 8x²

These cannot be combined:
3x² + 5x³
The first has x to the power of 2. The second has x to the power of 3.
These are unlike terms and must remain separate.

Example with several terms: 4x³ – 2x² + x³ + 6x²

Group x³ terms: 4x³ + x³ = 5x³
Group x² terms: -2x² + 6x² = 4x²
Result: 5x³ + 4x²

Never add exponents when combining like terms. The exponent stays exactly as it is. You only add or subtract the coefficients.

Like Terms With More Than One Variable

When a term contains more than one variable, every single variable in the term and its corresponding exponent must match for two terms to be like.

These are like terms:
3xy + 5xy
Both contain x to the power of 1 and y to the power of 1. Variable parts are identical.
Result: 8xy

These are like terms:
4x²y + 7x²y
Both contain x to the power of 2 and y to the power of 1.
Result: 11x²y

These are NOT like terms:
3xy and 3x²y
The first has x¹y. The second has x²y. The exponent on x differs.
They cannot be combined.

These are NOT like terms:
4xy² and 4x²y
The first has xy². The second has x²y. The entire variable configuration differs.
They cannot be combined.

The order in which variables are written does not matter. 3xy and 5yx are like terms because xy and yx represent the same product. By convention, variables are usually written in alphabetical order.

Constants as Like Terms

Constants are numbers that stand alone without any variable. All constants are like terms with each other because they all share the same “variable part,” which is no variable at all.

Examples:

5 + 7 = 12

-3 + 8 = 5

4 + (-9) + 2 = -3

In an expression such as 3x + 4 + 7x – 2, the constants 4 and -2 are like terms with each other, and 3x and 7x are like terms with each other.

3x + 7x = 10x
4 – 2 = 2

Result: 10x + 2

Zero Coefficients and Like Terms

A term with a coefficient of zero is equal to zero, regardless of the variable attached to it.

0x = 0

For practical purposes in simplification, if a term simplifies to a zero coefficient, that term disappears from the expression.

Example: 5x – 5x = 0x = 0

This means the x terms cancel completely. The result is simply zero, which contributes nothing to the expression.

Understanding this helps when checking whether two like terms cancel each other out, which is a useful technique when solving equations.

Like Terms in Algebraic Expressions

Algebraic expressions are made up of terms connected by addition or subtraction. Identifying and combining like terms is one of the key steps in simplifying any algebraic expression.

For example, the expression 4x + 3y – x + 2y might look complicated at first glance, but once you identify the like terms and combine them, it becomes much simpler:

4x – x = 3x
3y + 2y = 5y

Result: 3x + 5y

The article [What Is an Algebraic Expression?] explains the structure of algebraic expressions in detail, including how terms, variables, coefficients, and constants all work together. Reading it alongside this article will give you a complete understanding of how expressions are built and simplified.

Like Terms and Linear Equations

Like terms appear frequently on both sides of linear equations. Combining them is often the first simplification step when solving an equation.

Consider this equation:

3x + 2x + 4 = 14

Before solving for x, combine the like terms on the left:
3x + 2x = 5x

The equation becomes:
5x + 4 = 14

Now it is straightforward to solve: 5x = 10, so x = 2.

The article [What Is a Linear Equation?] covers how to solve linear equations step by step, and combining like terms is one of the most important techniques in that process.

Like Terms and Quadratic Equations

Quadratic expressions frequently contain terms that need to be combined before the expression can be factored or before the equation can be solved.

Consider this expression:

3x² + 5x – 2x² + 7x

Group and combine the like terms:
3x² – 2x² = x²
5x + 7x = 12x

Simplified result: x² + 12x

This kind of simplification is often necessary before factoring or applying the quadratic formula. The article [What Is a Quadratic Equation?] explains quadratic equations in full and shows where simplification fits into the solving process.

Like Terms and Factors

It is easy to confuse terms and factors, but they are different things.

A term is a single unit in an algebraic expression, separated from other terms by addition or subtraction signs.

A factor is a quantity that multiplies another quantity within a single term.

In the term 3x:

• 3x is one term.
• 3 and x are the two factors of that term.

Like terms are terms that share the same variable factors raised to the same powers. They are not the same as factors.

The article [What Is a Factor?] explains factors clearly and shows how they are used across different areas of mathematics. Understanding the distinction between factors and terms prevents one of the most common conceptual errors in algebra.

Like Terms and Fractions

Terms with fractional coefficients can absolutely be like terms, as long as their variable parts match.

Example: 1/2x and 3/4x

Both terms have the variable x to the power of 1. They are like terms.

To combine them, add the fractions:
1/2 + 3/4 = 2/4 + 3/4 = 5/4

Result: 5/4 x (or equivalently, 1.25x)

The fraction arithmetic follows standard rules. The article [What Is a Fraction?] provides a thorough explanation of how fractions work, including how to add fractions with different denominators, which is directly relevant to combining like terms with fractional coefficients.

Like Terms and Rational Numbers

Coefficients of like terms can be any rational number. This includes whole numbers, negative integers, fractions, and terminating or repeating decimals.

Example: 1/3x + 2/5x

These are like terms because both contain x to the power of 1.

Find a common denominator to add the fractions:
1/3 + 2/5 = 5/15 + 6/15 = 11/15

Result: 11/15 x

Rational number coefficients are perfectly valid in algebra and do not change the fundamental rule: if the variable parts are the same, the terms are like terms and can be combined.

The article [What Is a Rational Number?] explains what rational numbers are and how fraction arithmetic works, both of which are directly useful when working with algebraic terms that have rational coefficients.

Like Terms and Real Numbers

Coefficients in algebraic expressions can be any real number. This includes integers, fractions, decimals, and even irrational numbers such as π or √2, though these are less common at introductory levels.

The important point is that whether or not two terms are like terms is determined entirely by their variable parts, not by the nature of their coefficients. A term with a coefficient of √3 and a term with a coefficient of 5 are still like terms if they share the same variable part.

The article [What Is a Real Number?] explains the complete real number system in a clear and accessible way, helping you understand the full range of values that coefficients can take.

Like Terms in Physics Formulas

Algebraic terms appear throughout physics formulas, and the ability to identify and combine like terms is just as useful in scientific contexts as it is in pure mathematics.

For example, if you are working with expressions involving force, mass, and acceleration, you may encounter situations where multiple terms with the same variable need to be combined before substituting values. Understanding the article [What Is Force in Physics?] provides useful context for how algebraic expressions are used to model physical quantities, and how simplification skills transfer directly to scientific problem-solving.

Step-by-Step Examples

The following section provides fifteen fully worked examples, covering every type of like-term situation you are likely to encounter.

Worked Example 1

Given: 3x + 7x

Identify Like Terms: Both terms contain x to the power of 1.

Combine Terms: 3 + 7 = 10

Final Answer: 10x

Worked Example 2

Given: 8a – 3a + 5

Identify Like Terms: 8a and -3a are like terms. The constant 5 stands alone.

Combine Terms: 8a – 3a = 5a. The constant 5 remains unchanged.

Final Answer: 5a + 5

Worked Example 3

Given: 4x² + 7x – 2x² + 3x

Identify Like Terms: 4x² and -2x² are like terms. 7x and 3x are like terms.

Combine Terms:
4x² – 2x² = 2x²
7x + 3x = 10x

Final Answer: 2x² + 10x

Worked Example 4

Given: 5xy + 3x – 2xy + 7x

Identify Like Terms: 5xy and -2xy are like terms. 3x and 7x are like terms.

Combine Terms:
5xy – 2xy = 3xy
3x + 7x = 10x

Final Answer: 3xy + 10x

Worked Example 5

Given: 1/2x + 3/4x

Identify Like Terms: Both contain x to the power of 1.

Combine Terms: 1/2 + 3/4 = 2/4 + 3/4 = 5/4

Final Answer: 5/4 x

Worked Example 6

Given: 0.5a + 1.5a

Identify Like Terms: Both contain a to the power of 1.

Combine Terms: 0.5 + 1.5 = 2

Final Answer: 2a

Worked Example 7

Given: 6m³ – 2m³ + 4m²

Identify Like Terms: 6m³ and -2m³ are like terms. 4m² has no matching term.

Combine Terms: 6m³ – 2m³ = 4m³. The term 4m² remains unchanged.

Final Answer: 4m³ + 4m²

Worked Example 8

Given: 3x + 4y – x + 2y – 5

Identify Like Terms: 3x and -x. 4y and 2y. -5 is a constant alone.

Combine Terms:
3x – x = 2x
4y + 2y = 6y

Final Answer: 2x + 6y – 5

Worked Example 9

Given: -4ab + 6ab – 3ab

Identify Like Terms: All three are like terms (contain ab).

Combine Terms: -4 + 6 – 3 = -1

Final Answer: -ab

Worked Example 10

Given: 2x²y + 5xy² – 3x²y

Identify Like Terms: 2x²y and -3x²y are like terms. 5xy² has no matching term.

Combine Terms: 2x²y – 3x²y = -x²y. The term 5xy² remains.

Final Answer: -x²y + 5xy²

Worked Example 11

Given: 7 – 3 + 2x – 9 + x

Identify Like Terms: Constants 7, -3, -9. Variable terms 2x, x.

Combine Terms:
7 – 3 – 9 = -5
2x + x = 3x

Final Answer: 3x – 5

Worked Example 12

Given: 1/3a² + 2/3a²

Identify Like Terms: Both contain a to the power of 2.

Combine Terms: 1/3 + 2/3 = 3/3 = 1

Final Answer: a²

Worked Example 13

Given: 5x – 5x + 3y

Identify Like Terms: 5x and -5x. 3y stands alone.

Combine Terms: 5x – 5x = 0

Final Answer: 3y

Worked Example 14

Given: 4p + 3q – 2p + q – p

Identify Like Terms: 4p, -2p, -p are like terms. 3q, q are like terms.

Combine Terms:
4p – 2p – p = (4 – 2 – 1)p = p
3q + q = 4q

Final Answer: p + 4q

Worked Example 15

Given: 3.2x² + 1.8x² – 0.5x + 2.5x

Identify Like Terms: 3.2x² and 1.8x². -0.5x and 2.5x.

Combine Terms:
3.2 + 1.8 = 5 → 5x²
-0.5 + 2.5 = 2 → 2x

Final Answer: 5x² + 2x

Common Mistakes Students Make

Mistake 1: Combining x and y
Incorrect: 3x + 4y = 7xy
Correct: 3x + 4y remains as 3x + 4y (unlike terms)

Mistake 2: Combining x and x²
Incorrect: 3x + 5x² = 8x³
Correct: 3x + 5x² remains as 3x + 5x² (different exponents)

Mistake 3: Adding exponents instead of coefficients
Incorrect: 4x² + 3x² = 7x⁴
Correct: 4x² + 3x² = 7x² (only add the coefficients, never the exponents)

Mistake 4: Assuming coefficients must be equal
Incorrect assumption: 5x and 3x are not like terms because 5 ≠ 3
Correct: 5x and 3x are like terms. Only the variable parts matter.

Mistake 5: Combining terms with different variable combinations
Incorrect: 3xy + 4x = 7x²y
Correct: 3xy and 4x are unlike terms. They cannot be combined.

Mistake 6: Losing negative signs
Incorrect: 5x – 8x = 13x
Correct: 5x – 8x = -3x (the coefficient is -8, not 8)

Mistake 7: Combining a constant with a variable term
Incorrect: 3x + 5 = 8x
Correct: 3x and 5 are unlike terms. The result stays as 3x + 5.

Mistake 8: Confusing factors with terms
Incorrect thinking: In 6x, the terms are 6 and x.
Correct: In 6x, there is only one term. 6 and x are its factors, not separate terms.

Mistake 9: Assuming every expression simplifies further
Some expressions such as 3x + 4y + 2 are already fully simplified because all three terms are unlike.

Like Terms Rules Cheat Sheet

Like Terms vs Factors

This is a distinction that confuses many students, so let us make it very clear.

A term is a unit in an algebraic expression separated from other units by a + or – sign.

A factor is one of the quantities that are multiplied together within a single term.

In the term 3x:

• The entire expression 3x is a single term.
• The numbers 3 and x are the two factors of that term. They are multiplied together.

In the expression 3x + 5x:

• There are two terms: 3x and 5x.
• Each term has two factors (3 and x in the first; 5 and x in the second).
• These are like terms because their variable factors (x) are identical.

Like terms are about what is being added or subtracted. Factors are about what is being multiplied within a term. These are two completely different operations.

Like Terms vs Terms

A term is any single algebraic component in an expression. It can be a variable term like 5x, a multi-variable term like 3xy, or a constant like 7.

Like terms are a subcategory of terms. They are terms that share identical variable parts and can therefore be combined.

Not all terms in an expression are like terms. In 3x + 4y – 5, there are three terms, but none of them are like terms of each other. The expression is already in its simplest form.

Like Terms Practice Questions

20 Multiple Choice Questions

Question 1: Which pair of terms are like terms?
A) 3x and 3x²
B) 5a and 5b
C) 4y and 9y
D) 2xy and 2x

Correct Answer: C
Explanation: 4y and 9y both contain y to the power of 1. Their coefficients differ but their variable parts are identical.

Question 2: What is 6x + 4x?
A) 10x²
B) 24x
C) 10x
D) 2x

Correct Answer: C
Explanation: Add the coefficients: 6 + 4 = 10. The variable x stays unchanged. Result: 10x.

Question 3: Which of the following pairs are NOT like terms?
A) 7m² and -3m²
B) 2ab and 5ab
C) 4x and 4y
D) -p and 8p

Correct Answer: C
Explanation: 4x and 4y have different variables (x versus y), so they are unlike terms.

Question 4: Simplify 9a – 4a + a.
A) 5a
B) 6a
C) 14a
D) 4a

Correct Answer: B
Explanation: 9 – 4 + 1 = 6. Result: 6a.

Question 5: Are x² and x³ like terms?
A) Yes, because both contain x
B) No, because they have different exponents
C) Yes, because their coefficients are the same
D) No, because they are both powers

Correct Answer: B
Explanation: Like terms must have identical exponents. x² has exponent 2 and x³ has exponent 3. They are unlike terms.

Question 6: Simplify 5x + 3y – 2x + y.
A) 7xy
B) 3x + 4y
C) 3x – 4y
D) 7x + 4y

Correct Answer: B
Explanation: 5x – 2x = 3x. 3y + y = 4y. Result: 3x + 4y.

Question 7: What is the result of 3xy + 8xy?
A) 11x²y²
B) 24xy
C) 11xy
D) 11x + y

Correct Answer: C
Explanation: Both terms have the variable part xy. 3 + 8 = 11. Result: 11xy.

Question 8: Can constants such as 5 and -3 be combined?
A) No, constants cannot be combined.
B) Yes, because they have no variable part.
C) Only if they are both positive.
D) Only if they are both negative.

Correct Answer: B
Explanation: Constants are always like terms. 5 + (-3) = 2.

Question 9: Which expression is fully simplified?
A) 4x + 3x + 2y
B) 7x + 2y
C) Both A and B represent the same expression
D) Neither

Correct Answer: C
Explanation: 4x + 3x = 7x, so 4x + 3x + 2y simplifies to 7x + 2y. Both are equivalent.

Question 10: Simplify 7a² – 2a² + 3a.
A) 8a² + 3a
B) 5a² + 3a
C) 5a³ + 3a
D) 8a³

Correct Answer: B
Explanation: 7a² – 2a² = 5a². The term 3a is unlike and remains. Result: 5a² + 3a.

Question 11: What is 1/2x + 1/2x?
A) 1/4x
B) x
C) 2x
D) 1x²

Correct Answer: B
Explanation: 1/2 + 1/2 = 1. Result: 1x = x.

Question 12: Are 3x²y and 3xy² like terms?
A) Yes, because they both contain x and y
B) No, because the exponents on x and y differ
C) Yes, because the coefficients are equal
D) No, because they have three variables

Correct Answer: B
Explanation: 3x²y has x² and y. 3xy² has x and y². The exponent positions differ, so they are unlike terms.

Question 13: Simplify 5p – 5p + 3q.
A) 3pq
B) 10p + 3q
C) 3q
D) 0

Correct Answer: C
Explanation: 5p – 5p = 0. Only 3q remains.

Question 14: Which correctly combines -4m and 7m?
A) -3m
B) 3m
C) 11m
D) -28m²

Correct Answer: B
Explanation: -4 + 7 = 3. Result: 3m.

Question 15: In the expression 4x + 7y – 2x + 3, which terms are like terms?
A) 4x and 7y
B) 4x and -2x
C) 7y and 3
D) All terms

Correct Answer: B
Explanation: 4x and -2x both contain x to the power of 1. They are like terms.

Question 16: Simplify 0.4a + 1.6a.
A) 1.2a
B) 2a
C) 0.64a
D) 2a²

Correct Answer: B
Explanation: 0.4 + 1.6 = 2. Result: 2a.

Question 17: Which statement about like terms is correct?
A) They must have identical coefficients.
B) They must have identical variable parts.
C) They must have the same number of terms.
D) They must all be positive.

Correct Answer: B
Explanation: Like terms must have identical variable parts (same variables and same exponents). Coefficients can differ.

Question 18: Simplify 6mn – 4mn + 2mn.
A) 4m²n²
B) 12mn
C) 4mn
D) -4mn

Correct Answer: C
Explanation: 6 – 4 + 2 = 4. Result: 4mn.

Question 19: Is 5x a single term or two terms?
A) Two terms: 5 and x
B) One term with two factors
C) Two like terms
D) A constant

Correct Answer: B
Explanation: 5x is a single algebraic term. 5 and x are its factors, not separate terms.

Question 20: Simplify 3a + 2b – a + 5b – 4.
A) 2a + 7b – 4
B) 3a + 7b
C) 4a + 3b
D) 2a – 7b + 4

Correct Answer: A
Explanation: 3a – a = 2a. 2b + 5b = 7b. The constant -4 remains. Result: 2a + 7b – 4.

10 Identify Like Terms Questions

Q1: From the expression 3x + 4y – 2x + y, identify the groups of like terms.
Answer: Like terms: {3x, -2x} and {4y, y}.

Q2: In 5a² + 3a – a² + 7, which terms are like terms?
Answer: {5a², -a²} are like terms. {3a} and {7} each stand alone with no matching partner.

Q3: From 2xy + 4x – xy + 3y, identify the like terms.
Answer: {2xy, -xy} are like terms. 4x and 3y each stand alone.

Q4: In 6m³ + 2m² – 4m³ + m, which are like terms?
Answer: {6m³, -4m³} are like terms. {2m²} and {m} each stand alone.

Q5: Identify like terms in 1/2p + 3p – 2q + q.
Answer: {1/2p, 3p} are like terms. {-2q, q} are like terms.

Q6: From 4a²b + 3ab² – a²b, identify the like terms.
Answer: {4a²b, -a²b} are like terms. {3ab²} stands alone.

Q7: In 9 – 4x + 6 + 2x – 1, which terms are like?
Answer: {9, 6, -1} are constant like terms. {-4x, 2x} are like terms.

Q8: From 5x²y – 2xy² + x²y, identify the like terms.
Answer: {5x²y, x²y} are like terms. {-2xy²} stands alone.

Q9: In 3c + 2d – 5c + d + 4, which terms are like?
Answer: {3c, -5c} are like terms. {2d, d} are like terms. {4} is a constant alone.

Q10: From 7n² + 3n – 5n² + n² – 2n, identify the like terms.
Answer: {7n², -5n², n²} are like terms. {3n, -2n} are like terms.

10 Simplification Problems

Problem 1: 5x + 3x – 2x
Solution: (5 + 3 – 2)x = 6x

Problem 2: 4a + 3b – a + 7b
Solution: (4a – a) + (3b + 7b) = 3a + 10b → 3a + 10b

Problem 3: 6x² + 2x – 4x² + 5x
Solution: (6x² – 4x²) + (2x + 5x) = 2x² + 7x → 2x² + 7x

Problem 4: 2xy – 5xy + 3x
Solution: (2xy – 5xy) + 3x = -3xy + 3x → -3xy + 3x

Problem 5: 8 – 3a + 4 – 2a
Solution: (-3a – 2a) + (8 + 4) = -5a + 12 → -5a + 12

Problem 6: 1/4m + 3/4m – m
Solution: (1/4 + 3/4 – 1)m = (4/4 – 1)m = 0m = 0

Problem 7: 3p² + 2p – p² – 5p + 4
Solution: (3p² – p²) + (2p – 5p) + 4 = 2p² – 3p + 4 → 2p² – 3p + 4

Problem 8: 0.6x + 1.4x + 3y – y
Solution: 2x + 2y → 2x + 2y

Problem 9: 5a²b – 2a²b + ab
Solution: (5 – 2)a²b + ab = 3a²b + ab → 3a²b + ab

Problem 10: 9 – 4n + 3n² – 5 + n – n²
Solution: (3n² – n²) + (-4n + n) + (9 – 5) = 2n² – 3n + 4 → 2n² – 3n + 4

5 Challenge Questions

Challenge 1: Simplify 3(2x + 4) – 2(x – 1)
Solution: 6x + 12 – 2x + 2 = (6x – 2x) + (12 + 2) = 4x + 14

Challenge 2: Simplify 5a²b – 3ab² + 2a²b – ab² + 4ab
Solution: (5a²b + 2a²b) + (-3ab² – ab²) + 4ab = 7a²b – 4ab² + 4ab → 7a²b – 4ab² + 4ab

Challenge 3: Simplify 2(x² + 3x) – (x² – x) + 4x
Solution: 2x² + 6x – x² + x + 4x = (2x² – x²) + (6x + x + 4x) = x² + 11x

Challenge 4: Simplify 1/2x² + 3/4x² – 1/4x² + x
Solution: (2/4 + 3/4 – 1/4)x² + x = 4/4x² + x = x² + x

Challenge 5: Simplify 4(a + b) – 3(a – 2b) + b
Solution: 4a + 4b – 3a + 6b + b = (4a – 3a) + (4b + 6b + b) = a + 11b

Exam Tips

• Ignore coefficients when checking. When deciding whether two terms are like, look only at the variable parts. Coefficients are irrelevant for this check.
• Compare every variable. In multi-variable terms, every single variable in the term must match, not just one of them.
• Check every exponent. Even if the variables match, the exponents on each variable must also match. x² and x³ are not like terms.
• Keep signs attached to coefficients. In 5x – 3x, the coefficient of the second term is -3, not 3. The sign is part of the coefficient.
• Group like terms before combining. In a complex expression, write the like terms next to each other first. This reduces errors.
• Do not combine unlike terms. If the variable parts do not match, leave the terms exactly as they are. A simplified expression may still have several terms.
• Double-check the final expression. After combining, scan the result for any further like terms you may have missed.
• Never add or multiply the exponents. When combining like terms, only the coefficients change. The variable and its exponent stay exactly the same.

Quick Revision Notes

Definition of like terms: Algebraic terms that have identical variable parts, meaning the same variables each raised to the same exponents.

Like terms: 3x and 7x. 5a² and -2a². 4xy and 9xy.

Unlike terms: 3x and 4y. x and x². 5xy and 5x.

Coefficients: The numerical part in front of the variable. Coefficients can differ in like terms.

Variables: The letter or letters in a term. Every variable and its exponent must match exactly for terms to be like.

Exponents: The powers on each variable. A difference in any exponent makes terms unlike.

Combining like terms: Add or subtract the coefficients. Keep the variable part unchanged.

Constants: Numbers with no variable. All constants are like terms with each other.

Common mistakes: Adding exponents, combining unlike variables, losing negative signs, confusing factors with terms.

Like Terms Cheat Sheet

Frequently Asked Questions

1. What are like terms in algebra?
Like terms are algebraic terms that have exactly the same variables raised to exactly the same powers. Only their numerical coefficients may differ.

2. How do you identify like terms?
Compare the variable parts of each term, ignoring the coefficients. If every variable and every exponent matches exactly, the terms are like terms.

3. What is an example of like terms?
3x and 7x are like terms. Both contain x to the power of 1. Their coefficients (3 and 7) are different, but that does not matter.

4. What are unlike terms?
Unlike terms are terms whose variable parts are different. For example, 3x and 4y are unlike terms because x and y are different variables.

5. Can coefficients be different in like terms?
Yes, absolutely. The coefficients do not need to be the same. It is the variable parts that must be identical.

6. Can x and x² be like terms?
No. Although they share the variable x, the exponents differ (1 and 2). Like terms require identical exponents on every variable.

7. Can xy and yx be like terms?
Yes. xy and yx represent the same product. The order in which variables are written does not affect whether terms are like.

8. Can constants be like terms?
Yes. All constants are like terms because they all share the property of having no variable. For example, 5 and -3 can be combined to give 2.

9. How do you combine like terms?
Add or subtract the coefficients of the like terms while keeping the variable part completely unchanged.

10. Why can unlike terms not be combined?
Unlike terms represent different algebraic quantities. Just as you cannot add apples and oranges to get a single type of fruit, you cannot add x and y into a single term.

11. Are fractions allowed in like terms?
Yes. Terms with fractional coefficients are like terms if their variable parts match. For example, 1/2x and 3/4x are like terms.

12. Are negative terms like terms?
A negative coefficient does not affect whether two terms are like. -3x and 5x are like terms because their variable parts are identical.

13. What is the difference between terms and factors?
A term is a unit in an expression separated by + or – signs. A factor is one of the quantities multiplied together within a single term. In 3x, 3x is the term, and 3 and x are its factors.

14. Can terms with multiple variables be like terms?
Yes, but the entire variable part must match exactly. 3xy and 7xy are like terms. However, 3xy and 7x²y are not, because the exponent on x differs.

15. How do like terms help simplify algebraic expressions?
Combining like terms reduces the number of terms in an expression, making it shorter, cleaner, and easier to work with when solving equations or substituting values.

Summary

Like terms in algebra are terms that share exactly the same variables, each raised to exactly the same exponents. The coefficients in front of the variables can be any numbers, positive, negative, fractional, or decimal, without affecting whether two terms are like.

To combine like terms, simply add or subtract their coefficients while leaving the variable part unchanged. This is the central technique in simplifying algebraic expressions.

Unlike terms have different variable parts and cannot be combined into a single term. Recognising the difference between like and unlike terms prevents some of the most common algebra errors students make.

Constants are always like terms with each other. Multi-variable terms are like terms only if every variable and every exponent in the variable part matches exactly. Expressions with all unlike terms are already fully simplified.

Final Thoughts

Recognising what are like terms in algebra is one of the most important foundational skills you will develop in mathematics. Almost every area of algebra, from simplifying expressions to solving linear equations, working with quadratics, and factoring polynomials, requires the ability to identify and combine like terms confidently.

The skill is not complicated. Two terms are like terms if their variable parts are identical. Add or subtract the coefficients, and keep the variable part as it is. That is all there is to it.

Practise with a wide range of expressions, including those with multiple variables, fractional coefficients, negative values, and exponents. The more variety you work through, the more automatic the recognition becomes. Once you can identify and combine like terms instantly, every topic that builds on this skill becomes considerably easier.

References

1. OpenStax – Elementary Algebra and Prealgebra textbooks covering like terms, algebraic expressions, and simplification.
   https://openstax.org
2. Khan Academy – Free lessons and exercises on identifying and combining like terms in algebraic expressions.
   https://www.khanacademy.org
3. Mathematics LibreTexts – Open-access mathematics library with detailed coverage of algebraic terms, coefficients, and simplification.
   https://math.libretexts.org
4. Encyclopaedia Britannica – Reference articles on algebra, algebraic terms, and the foundations of symbolic mathematics.
   https://www.britannica.com
5. Wolfram MathWorld – Comprehensive mathematical reference covering algebraic expressions, like terms, and polynomial simplification.
   https://mathworld.wolfram.com

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