Combining Like Terms

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

Intermediate25 minLesson
Printable worksheet

Definition

Like terms are terms that have the same variable raised to the same power. Only like terms can be combined.
For example:
  • 3x3x and 5x5x are like terms (both have xx)
  • 4y24y^2 and −2y2-2y^2 are like terms (both have y2y^2)
  • 77 and −3-3 are like terms (both are constants)
To combine like terms, add or subtract their coefficients while keeping the variable the same:
3x+5x=8x3x + 5x = 8x
7y−2y=5y7y - 2y = 5y
4a+3b+2a=6a+3b4a + 3b + 2a = 6a + 3b

Try it now

Simplify: 5x+3x5x + 3x

Worked Examples

Simplify: 4x+7x4x + 7x
1

Identify like terms

Both 4x4x and 7x7x have the same variable xx → Like terms
2

Add the coefficients

4+7=114 + 7 = 11
3

Keep the variable

Write xx after the sum → 11x11x

Common Mistakes

Adding variables: 3x+5x=8x23x + 5x = 8x^2

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

Correct: 3x+5x=8x3x + 5x = 8x (think: 3 apples + 5 apples = 8 apples)

Combining unlike terms: 3x+4y=7xy3x + 4y = 7xy

Why it's wrong: xx and yy are different variables, so 3x3x and 4y4y cannot be combined.

Correct: 3x+4y3x + 4y is already simplified (these are unlike terms)

Forgetting that x=1xx = 1x

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

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

Treating xx and x2x^2 as like terms

Why it's wrong: xx and x2x^2 have different powers, so they are NOT like terms.

Correct: x+x2x + x^2 cannot be simplified further

Interactive Visual

Algebra tiles: combining like terms

Each tile is a term: big squares are x², long strips are x, small squares are 1. Red tiles are negative.

5x25x^2
3x3x
2x22x^2
−x-x

5x2+3x+2x2−x5x^2 + 3x + 2x^2 - x

Every term becomes tiles: the coefficient tells how many.

=x2= x^2=x= x=1= 1negative

Function graph

-3-2-10123-20-100102030xy

Tap or hover over the graph to read off values.

2x + 5 + 6x - 38x + 2

Table of values

x0123
2x + 5 + 6x - 32101826
8x + 22101826

Interactive Sandbox

Expression Calculator

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History

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Practice Problems

16 problems
Problem 1 of 16
Easy
Simplify: 5x+3x5x + 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=203x + 5 + 2x = 20, you need to combine to get 5x+5=205x + 5 = 20
  • Real-world calculations: Calculating total costs, like 3 notebooks at xx each plus 2 more notebooks: 3x+2x=5x3x + 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 pp dollars each, then 5 more pens. Total cost: 3p+5p=8p3p + 5p = 8p dollars.

1Try It Yourself

A student buys 4 notebooks for nn dollars each, 3 folders for ff dollars each, then 2 more notebooks and 1 more folder.

Write and simplify an expression for the total cost.

Step 1: Choose the right answer

Simplify the total 4n+3f+2n+f4n + 3f + 2n + f:

Sports Statistics

Combining points scored in different games.

Example:

A basketball player scores pp points in the first half and 2p2p points in the second half. Total: p+2p=3pp + 2p = 3p points.

2Try It Yourself

A football team scores gg goals in its first match and 3g3g goals in its second match. Over the two matches it concedes 2g2g goals.

Write the team's goal difference (goals scored minus goals conceded) as a simplified expression.

Step 1: Choose the right answer

Simplify g+3g−2gg + 3g - 2g:

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=1xx = 1x)

Frequently Asked Questions

No! 2x2x and 3y3y have different variables, so they are unlike terms and cannot be combined. 2x+3y2x + 3y is already fully simplified.
No! 2x2x and 3y3y have different variables, so they are unlike terms and cannot be combined. 2x+3y2x + 3y is already fully simplified.
Think of it like counting objects: 1 apple + 1 apple = 2 apples, not 1 apple-squared. The exponent stays the same when combining like terms.
The coefficient is −1-1. When there's no number in front of a variable, it's 1 (or −1-1 if there's a minus sign).

Glossary

Like terms
Terms with the same variable raised to the same power (e.g., 3x3x and 5x5x, or 2y22y^2 and −4y2-4y^2)
Coefficient
The number multiplied by a variable (e.g., in 7x7x, 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., 55, xx, or 3x23x^2)
Simplify
To reduce an expression by combining like terms
Today's challengeOne problem, three tries

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