1.5 Simplifying Algebraic Expressions
Learning Objectives
- Combine like terms.
- Apply the distributive property to simplify expressions.
Launch
When simplifying expressions (not solving equations), we combine like terms to rewrite the expression in a simpler form.
Combine Like Terms
An algebraic expression is made up of terms—parts separated by plus or minus signs.
- A coefficient is the number multiplying a variable (example: in
, the coefficient is 7). - Like terms have the same variable raised to the same power. Their coefficients may be different.
- Example:
and 
are like terms. - Example:
and 
are like terms. - Example:
and 
are not like terms (different variables).
- Example:
📌 Rule: To combine like terms, add or subtract their coefficients. The variable part stays the same.
Example 1.5.1
Simplify: 
Solution
Both terms are like terms (same variable 
).
Example 1.5.2
Simplify: 
Solution
Group like terms:
Example 1.5.3
Simplify: 
Solution
and 
are like terms.
is not like them (different power).
Try It
Apply the Distributive Property to Simplify
Recall that the distributive property says:
We often use it to remove parentheses, then combine like terms to simplify further.
In an earlier lesson, we simplified expressions like 
to get 
.
Here, we apply the distributive property in more involved expressions.
Example 1.5.4
Simplify: 
Solution
Distribute:
Optional step is to write the liker terms beside each other (you don’t need to include parentheses–just did this so you could see how they were being “grouped”.)
Example 1.5.5
Simplify: 
Solution
Distribute:
Optional step of writing the like terms beside each other.
Example 1.5.6
Simplify: 
Solution
Distribute:
(Optional step: change the subtraction to “plus a negative”. We will often write the negative term with a parentheses around it–but this is not required.)
Try It
Key Takeaways
- Like terms have the same variable raised to the same power. Combine them by adding or subtracting coefficients.
- The distributive property removes parentheses and allows us to combine terms.
- Always simplify expressions by distributing first, then combining like terms.
