What Does It Mean to Simplify an Expression?

To simplify an expression means to rewrite it in the most compact or efficient form—without changing its value. This involves combining like terms, applying the distributive property, and removing any unnecessary parentheses.

This is a foundational skill in algebra that helps prepare expressions for solving equations and inequalities later.

Key Concepts

1. Like Terms

• Like terms are terms that have the same variable(s) raised to the same powers.
  
  

• You can only combine like terms by adding or subtracting their coefficients.
  
  

Examples:

• 3x3x3x and −5x-5x−5x are like terms → 3x−5x=−2x3x - 5x = -2x3x−5x=−2x
  
  

• 2x22x^22x2 and 7x7x7x are not like terms
  
  

2. The Distributive Property

The distributive property allows you to multiply a single term across terms inside parentheses:

a(b+c)=ab+aca(b + c) = ab + aca(b+c)=ab+ac

Example:

3(x+4)=3x+123(x + 4) = 3x + 123(x+4)=3x+12

3. Combining Like Terms

Once all parentheses have been cleared using distribution, collect like terms to simplify further.

Example:

2x+3x−4=5x−42x + 3x - 4 = 5x - 42x+3x−4=5x−4

 Steps to Simplify Expressions

1. Distribute if there are parentheses.
   
   

2. Combine like terms (same variables and exponents).
   
   

3. Write the final simplified expression.
   
   

 Common Mistakes

• Combining unlike terms (e.g., xxx and x2x^2x2)
  
  

• Forgetting to distribute the negative sign
  
  

• Changing variables when combining (e.g., 3a+4b3a + 4b3a+4b → not combinable)
  
  

 Real-Life Connections

• Simplifying pricing formulas in business
  
  

• Cleaning up calculations in physics or engineering equations
  
  

• Estimating costs, taxes, or measurements in real-world projects