Lesson: Combining Like Terms

In this lesson, we will learn how to combine like terms in algebraic expressions. Like terms are terms that have the same variable raised to the same power.

Key Concepts

• Like Terms: Terms in an expression that have the same variable part. For example, in the expression $3x + 5x$, both terms are like terms because they both contain the variable $x$.
• Combining Like Terms: This process involves adding or subtracting the coefficients of like terms to simplify an expression.

Steps to Combine Like Terms

1. Identify Like Terms: Look for terms that have the same variable and exponent.
2. Add or Subtract Coefficients: For like terms, add or subtract their coefficients.
3. Write the Simplified Expression: Rewrite the expression with the combined like terms.

Example

Let's simplify the expression: $2x + 3x - 5 + 4$

Step 1: Identify like terms. Here, $2x$ and $3x$ are like terms. $-5$ and $4$ are constants.

Step 2: Combine the like terms:

• For $x$ terms: $2x + 3x = 5x$
• For constants: $-5 + 4 = -1$

Step 3: Write the simplified expression: $5x - 1$

Key Questions

• What are like terms?
• How do you combine like terms in an expression?
• Can you combine terms that have different variables or exponents?

Summary

Combining like terms is a fundamental skill in algebra that helps simplify expressions. Always look for terms that share the same variable and exponent to combine them effectively.