Combining Like Terms
Learn how to simplify algebraic expressions by combining terms with the same variable.
Definition
- and are like terms (both have )
- and are like terms (both have )
- and are like terms (both are constants)
Try it now
Worked Examples
Simplify:
Identify like terms
Both and have the same variable → Like terms
Add the coefficients
→
Keep the variable
Attach to the sum →
Answer:
Common Mistakes
Adding variables:
Why it's wrong: When combining like terms, we add COEFFICIENTS, not exponents. The variable stays the same.
Correct: (think: 3 apples + 5 apples = 8 apples)
Combining unlike terms:
Why it's wrong: and are different variables, so and cannot be combined.
Correct: is already simplified (these are unlike terms)
Forgetting that
Why it's wrong: A variable without a coefficient has an invisible coefficient of 1.
Correct:
Treating and as like terms
Why it's wrong: and have different powers, so they are NOT like terms.
Correct: cannot be simplified further
Interactive Visual
Balance Scale
Solution: x = 4
Interactive Sandbox
Expression Calculator
Try these:
History
No calculations yet
Practice Problems
16 problemsSimplify:
Why It Matters
- Simplifying equations: Before solving , you need to combine to get
- Real-world calculations: Calculating total costs, like 3 notebooks at each plus 2 more notebooks:
- 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 dollars each, then 5 more pens. Total cost: dollars.
A student buys 4 notebooks for dollars each, 3 folders for 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:
Sports Statistics
Combining points scored in different games.
Example:
A basketball player scores points in the first half and points in the second half. Total: points.
A team scores touchdowns in game 1, touchdowns in game 2, and loses touchdowns to penalties.
What is the final touchdown expression?
Step 1: Write the mathematical expression
Calculate:
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., )
Frequently Asked Questions
Glossary
- Like terms
- Terms with the same variable raised to the same power (e.g., and , or and )
- Coefficient
- The number multiplied by a variable (e.g., in , 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., , , or )
- Simplify
- To reduce an expression by combining like terms