Algebraic Expressions Lecture Notes

Overview

• Introduction to algebraic expressions and their types.
• Explanation of how to add and subtract different algebraic expressions.
• Basic properties of algebraic expressions.

Types of Algebraic Expressions

Monomial

• An algebraic expression with only one term.
• Examples:
  • 3x
  • 5x²
  • -7x
  • 11

Binomial

• An algebraic expression with two terms.
• Examples:
  • 2x - 3
  • 5x² - 7
  • 2x + 3x²
• Simplified example:
  • x² + 3x - 4x² can be simplified to -3x² + 3x (binomial form)

Trinomial

• An algebraic expression with three terms.
• Examples:
  • 5 - 3x + 7x²

Multinomial

• An algebraic expression with more than three terms.
• Examples:
  • 3 - 4x + 5x² + 7x³ - 9x⁴ + 12x⁵
• General: An expression with n terms (n > 3).

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: 5x (degree 1) and 7x³ (degree 3)

Adding Algebraic Expressions

1. Write all like terms of each expression one below the other.
2. Add the coefficients of like terms and write the exponent.

Example of Addition

• Expression A: 2x - 5 + 7x²
• Expression B: 4 + 3x - 2x²
• Sum: Rearrange in higher order and add:
  • A + B = 5x² + 5x - 1

Subtracting Algebraic Expressions

• Similar process to addition, but change signs of the expression being subtracted.

Example of Subtraction

• Expression A: 2x - 1 + x²
• Expression B: 2x² + 4x + 3
• Find A - B: Ensure like terms are in column-wise and change signs of B:
  • A - B = -x² - 2x - 4

Combining Addition and Subtraction

• Use the same steps for adding and subtracting multiple expressions.
• Example: A + B - C
  • First find A + B
  • Then subtract C from the result.

Conclusion

• Understanding the classification of algebraic expressions helps in simplifying expressions.
• Mastery of combining like terms, arranging terms, and applying rules of addition and subtraction is crucial for solving algebraic problems.