Lecture on Algebraic Expressions

Introduction

• Speaker: Jeff Jacobson of Anywhere Math
• Topic: Algebraic Expressions

What is an Algebraic Expression?

• Algebraic Expression: An expression that contains numbers, operations, and one or more variables.
• Numerical Expression: Contains numbers and operations but no variables.
• Key Point: Expressions do not have an equal sign; equations do.

Examples of Algebraic Expressions

• x ÷ 7
• 3x + 4
• xy (where xy implies multiplication)

Examples of Non-Algebraic Expressions

• 3 + 7 (No variable, numerical expression)
• 3x + 4 = 10 (Contains equal sign, which makes it an equation)

Key Vocabulary

Terms

• Terms: Parts of an expression separated by operations (e.g., in 5p + 4, terms are 5p and 4).

Coefficient

• Coefficient: The numerical factor of a term that includes a variable (e.g., in 5p, 5 is the coefficient).

Variable

• Variable: A symbol (usually a letter like x, y, or p) that represents one or more numbers. It can vary or change.

Constant

• Constant: A term with no variable, and it does not change (e.g., in 5p + 4, 4 is the constant).

Example 1: Identifying Parts of an Expression

• Expression: 5x + 13
  • Terms: 5x, 13
  • Coefficient: 5 (from term 5x)
  • Constant: 13

Example 2: Simplifying an Expression

• Expression: 1.5 × h × h × h
  • Simplified using exponents: 1.5h³
  • Coefficient: 1.5

Example 3: Evaluating an Expression

• Expression: 3x - 14 when x = 5
  • Step 1: Substitute 5 for x: 3(5) - 14
  • Step 2: Order of operations: 3 × 5 = 15
  • Step 3: Subtract: 15 - 14 = 1
  • Final Answer: 1

Practice Problems

• Speaker suggests trying more examples on your own and emphasizes the importance of practice.

Conclusion

• Encouragement to subscribe to the channel for more educational content.