Evaluating Algebraic Expressions

Introduction

• Focus on evaluating algebraic expressions.
• Result: a single numerical value.
• Values to use:
  • W = √5
  • X = -3
  • Y = 2
  • Z = 4
• Key concepts:
  • Use parentheses to ensure correct signs.
  • Follow the order of operations: "Please Excuse My Dear Aunt Sally":
    • Parentheses
    • Exponents
    • Multiplication and Division (left to right)
    • Addition and Subtraction (left to right)

Order of Operations

• Simplify inside parentheses first.
• Handle exponents next.
• Multiplication and division from left to right.
  • Example: 10 ÷ 2 × 3 = 15, not 5/3.
• Addition and subtraction from left to right.

Example 1: Evaluating 3x^2 + y - 7

• Substitute values:
  • 3(-3)^2 + 2 - 7
• Steps:
  • Exponents: (-3)^2 = 9
  • Multiplication: 3 × 9 = 27
  • Addition/Subtraction: 27 + 2 - 7 = 22
• Importance of showing work and using parentheses.

Example 2: Evaluating (YZ - X)^2

• Substitute values:
  • (2)(4) - (-3)
• Steps:
  • Simplify inside parentheses: 8 + 3 = 11
  • Exponents: 11^2 = 121

Example 3: Evaluating Y^2/(X + Z) - X^2/(Y - X)

• Substitute values:
  • (2)^2 / (-3 + 4) - (-3)^2 / (2 - (-3))
• Steps:
  • Simplify fractions using common denominators.
  • Result: 11/5 or 2 1/5 (mixed fraction)

Example 4: Evaluating W^2 - 3X

• Substitute values:
  • (√5)^2 - 3(-3)
• Steps:
  • Simplify exponents: √5 × √5 = 5
  • Multiplication: -3 × -3 = 9
  • Result: 5 + 9 = 14

Example 5: Absolute Value of 3X + Z^2

• Substitute values:
  • |3(-3) + 4^2|
• Steps:
  • Simplify: -9 + 16 = 7
  • Absolute value: |7| = 7

Conclusion

• Importance of careful evaluation and order of operations.
• Use of parentheses and understanding absolute values.
• Encouragement to practice and do homework.