Combining Like Terms

Learn how to simplify algebraic expressions by combining terms with the same variable.

Intermediate25 minLesson

Definition

Like terms are terms that have the same variable raised to the same power. Only like terms can be combined.

For example:

$3x$ and $5x$ are like terms (both have $x$ )
$4y^2$ and $-2y^2$ are like terms (both have $y^2$ )
$7$ and $-3$ are like terms (both are constants)

To combine like terms, add or subtract their coefficients while keeping the variable the same:

3x + 5x = 8x

7y - 2y = 5y

4a + 3b + 2a = 6a + 3b

Try it now

Simplify:

5x + 3x

Worked Examples

Simplify: $4x + 7x$

Identify like terms

Both $4x$ and $7x$ have the same variable $x$ → Like terms

Add the coefficients

$4 + 7 = 11$

Keep the variable

Attach $x$ to the sum → $11x$

Answer: $4x + 7x = 11x$

Common Mistakes

Adding variables: $3x + 5x = 8x^2$

Why it's wrong: When combining like terms, we add COEFFICIENTS, not exponents. The variable stays the same.

Correct: $3x + 5x = 8x$ (think: 3 apples + 5 apples = 8 apples)

Combining unlike terms: $3x + 4y = 7xy$

Why it's wrong: $x$ and $y$ are different variables, so $3x$ and $4y$ cannot be combined.

Correct: $3x + 4y$ is already simplified (these are unlike terms)

Forgetting that $x = 1x$

Why it's wrong: A variable without a coefficient has an invisible coefficient of 1.

Correct: $x + 5x = 1x + 5x = 6x$

Treating $x$ and $x^2$ as like terms

Why it's wrong: $x$ and $x^2$ have different powers, so they are NOT like terms.

Correct: $x + x^2$ cannot be simplified further

Interactive Visual

Balance Scale

x + 3=7

Apply to both sides:

Solution: x = 4

Interactive Sandbox

Expression Calculator

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History

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Practice Problems

16 problems

Problem 1 of 16

Easy

Simplify: $5x + 3x$

Why It Matters

Combining like terms is a fundamental skill in algebra that you'll use constantly:

Simplifying equations: Before solving $3x + 5 + 2x = 20$ , you need to combine to get $5x + 5 = 20$
Real-world calculations: Calculating total costs, like 3 notebooks at $x$ each plus 2 more notebooks: $3x + 2x = 5x$
Higher math: Every algebra course, from linear equations to calculus, requires this skill
Problem solving: Makes complex expressions easier to work with and understand

Real World Applications

Shopping and Budgets

Combining like items when calculating total costs.

Example:

You buy 3 pens at $p$ dollars each, then 5 more pens. Total cost: $3p + 5p = 8p$ dollars.

1Try It Yourself

A student buys 4 notebooks for $n$ dollars each, 3 folders for $f$ dollars each, then 2 more notebooks and 1 more folder.

Write and simplify an expression for the total cost.

Step 1: Write the mathematical expression

Write the total: $4n + 3f + 2n + f$

Sports Statistics

Combining points scored in different games.

Example:

A basketball player scores $p$ points in the first half and $2p$ points in the second half. Total: $p + 2p = 3p$ points.

2Try It Yourself

A team scores $t$ touchdowns in game 1, $3t$ touchdowns in game 2, and loses $2t$ touchdowns to penalties.

What is the final touchdown expression?

Step 1: Write the mathematical expression

Calculate: $t + 3t - 2t$

Key Takeaways

1Like terms have the same variable raised to the same power
2To combine like terms, add or subtract the coefficients
3Constants (numbers without variables) are like terms with each other
4Unlike terms (different variables or powers) cannot be combined
5A variable without a visible coefficient has coefficient 1 (e.g., $x = 1x$ )

Frequently Asked Questions

No!

2x

and

3y

have different variables, so they are unlike terms and cannot be combined.

2x + 3y

is already fully simplified.

Glossary

Like terms: Terms with the same variable raised to the same power (e.g., $3x$ and $5x$ , or $2y^2$ and $-4y^2$ )
Coefficient: The number multiplied by a variable (e.g., in $7x$ , the coefficient is 7)
Constant: A term without a variable (e.g., 5, -3, or 12)
Term: A single number, variable, or number times a variable (e.g., $5$ , $x$ , or $3x^2$ )
Simplify: To reduce an expression by combining like terms