Algebraic Expressions Lecture Notes

Introduction

• Topic: Algebraic Expressions
• Focus on expressing, adding, and subtracting algebraic expressions.
• Basic properties need to be understood first.

Types of Algebraic Expressions

1. Monomial

   • Definition: Algebraic expression with only one term.
   • Examples: 3x, 5x^2, -7x, 11.

2. Binomial

   • Definition: Algebraic expression with two terms.
   • Examples: 2x - 3, 5x^2 - 7, 2x + 3x^2.
   • Simplification can convert expressions to binomials.

3. Trinomial

   • Definition: Algebraic expression with three terms.
   • Example: 5 - 3x + 7x^2.

4. Multinomial

   • Definition: Algebraic expression with more than three terms.
   • Example: 3 - 4x + 5x^2 + 7x^3 - 9x^4 + 12x^5.

Like Terms and Unlike Terms

• Like Terms

  • Terms with the same degree.
  • Example: 3x and 4x (both degree 1).

• Unlike Terms

  • Terms with different degrees.
  • Example: 3x and 5x^2.

Adding Algebraic Expressions

• Step 1: Write all like terms one below the other.
• Step 2: Add coefficients of like terms, maintain degree.
• Example:
  • Expressions: A = 2x - 5 + 7x^2, B = 4 + 3x - 2x^2.
  • Rearrange and add like terms.
  • Result: 5x^2 + 5x - 1.

Subtraction of Algebraic Expressions

• Similar process as addition but change signs of the second expression.
• Example:
  • Expressions: A = 2x - 1 + x^2, B = 2x^2 + 4x + 3.
  • Subtract B from A.
  • Result: -x^2 - 2x - 4.

Mixed Operations (Addition and Subtraction)

• Combine addition and subtraction processes.
• Example:
  • Expressions: A = 2x^2 - 1 + 3x, B = 1 - x^3, C = 2x - 3.
  • Find A + B - C
  • Process: Add first, then subtract.
  • Result: -x^3 + 2x^2 + x + 3.

Conclusion

• Techniques can be extended to multiple expressions.
• Maintain chronological order and apply rules systematically.