Algebraic Expressions and Models

Introduction

• Today's focus: Algebraic expressions and models
• Instructor: Mr. Faust

Sample Problems

1. Evaluate without a calculator:
   • ((-2)^6): Negative 2 to the 6th power results in positive 64 due to even exponent.
   • (3^4): Equals 81.
   • (-2^6): Negative 64 because exponent does not affect negative sign.

Using Calculators

• Importance of parentheses:
  • Calculators require correct input of parentheses to distinguish expressions like ((-2)^6) from (-2^6).

Order of Operations (PEMDAS/GEMDAS)

• P: Parentheses or G: Grouping symbols
• E: Exponents
• MD: Multiplication and Division (left to right)
• AS: Addition and Subtraction (left to right)
• Mnemonic: "Please Excuse My Dear Aunt Sally"

Solving Problems

1. Example:
   • Simplify expressions inside parentheses first.
   • Resolve exponents.
   • Perform multiplication/division.
   • Complete addition/subtraction.

Evaluating Algebraic Expressions

• Substitution Method:
  • Plug in given values for variables (e.g., x = 2).
  • Also known as synthetic substitution in higher-level math.

Terminology

• Coefficient: The number before a variable (e.g., in 2x, 2 is the coefficient).
• Variable: Represents values that can change (e.g., x).
• Like Terms: Terms with the same variable and exponent (e.g., 2x and 3x).

Word Problems

• Example Problem:
  • Buying scented lotion or bath soap for 8 people.
  • Lotions = $6, Soaps = $5.
  • Write an expression for total cost:
    • Let S = number of soaps.
    • Number of lotions = 8 - S.
    • Cost equation: (5S + 6(8-S)).

Application of Concepts

• Solving real-world problems using algebraic expressions.
• Understand how to create equations based on word problems.

Conclusion

• Apply learned concepts to practice problems.
• Comment on learning experience.