Combining Like Terms
What You’ll Learn
Section titled “What You’ll Learn”In this lesson you’ll learn what “like terms” are and how to combine them to simplify algebraic expressions.
The Concept
Section titled “The Concept”Like terms have the same variable raised to the same power (e.g., and , or and , since constants are like terms with no variable).
To combine like terms: Add or subtract their coefficients, keep the variable the same.
Examples:
- (constants only)
Only combine terms that match exactly. and are not like terms.
Worked Examples
Section titled “Worked Examples”Simplify
- Group like terms:
- Combine:
Final simplified expression:
Real-World Applications
Section titled “Real-World Applications”Combining like terms helps simplify real costs or totals. Example: Weekly expenses = 45 dollars food + 30 dollars gas + 15 dollars snacks + 20 dollars coffee. Group: (45 + 15) food/snacks + 30 gas + 20 coffee = 60 dollars food/snacks + 30 gas + 20 coffee. Or total pay = 18 dollars/hour × h hours + 50 dollars bonus. Leave as is, but if multiple rates, combine like terms.