Substitution in Algebra

Introduction

• Definition: Substitution involves replacing a variable with a specific value in mathematical expressions.
• Importance of substitution in algebraic expressions.

Basic Substitution Example

• When x = 3:
  • Example: 2 + x
    • Substitute x with 3:
      • Calculation: 2 + 3 = 5

Working with Negative Numbers

• Replace x with -3:
  • Example: 2 + x
    • Substitute x with (-3):
      • Calculation: 2 + (-3)
      • This simplifies to 2 - 3 = -1.

Complicated Expressions

• Expression: 2x² - 10
  • Substitute x with (-3):
    • Calculation:
      • 2(-3)² - 10
      • (-3)² = 9
      • 2 × 9 = 18
      • 18 - 10 = 8

Quadratic Expression Example

• Expression: 2(x² - 3x + 5)
  • Substitute x with (-3):
    • Calculation:
      • (-3)² = 9
      • 2 × 9 = 18
      • (-3) × (-3) = 9
      • Final sum: 18 + 9 + 5 = 32.

Using Two Variables

• Expression: 2xy - 2xy²
  • Substitute x with (-3) and y with (-2):
    • Calculation:
      • 2(-3)(-2) - 2(-3)(-2)²
      • 2 × 3 × 2 = 12
      • (-2)² = 4
      • -2 × 3 × 4 = -24
      • Total: 12 - 24 = -12

Conclusion

• Recap on the process of substitution in algebra.
• Encouragement for students to practice substitution with various expressions.
• Reminder to ask questions if needed.