Algebra Class: Combining Like Terms

Combining Like Terms

Addition of Like Terms

• Definition: Like terms are terms that have identical variable parts.
• Process:
  • Identify the like terms in an expression (e.g., 3x and 5x).
  • Add their coefficients while keeping the variable the same (e.g., 3x + 5x = (3+5)x = 8x).
• Example:
  • 4a + 7a ➔ (4 + 7)a = 11a
  • 2x² + 3x² ➔ (2 + 3)x² = 5x²

Subtraction of Like Terms

• Process:
  • Identify the like terms (e.g., 9y and 4y).
  • Subtract their coefficients while keeping the variable the same (e.g., 9y - 4y = (9-4)y = 5y).
• Example:
  • 10m - 3m ➔ (10 - 3)m = 7m
  • 6p² - 2p² ➔ (6 - 2)p² = 4p²

Simplifying Expressions

• Definition: The process of reducing an expression to its simplest form by combining like terms.

• Steps:

  1. Identify all like terms in the expression.
  2. Add or subtract the coefficients of like terms as appropriate.
  3. Rewrite the expression with the simplified terms.

• Example:

  • Simplify 3a + 4b - 2a + 5b:
    • Combine like terms (3a - 2a) and (4b + 5b).
    • Result: (3-2)a + (4+5)b = 1a + 9b = a + 9b.

• Key Notes:

  • Always keep the variable part constant while adding or subtracting.
  • Coefficients alone can be manipulated without altering the variable.
  • This process helps in solving equations efficiently.

Combining Like Terms

• Like terms have identical variable parts.
• Adding like terms: Add the coefficients of like terms while keeping the variable the same.
  • Example: 3x + 5x = (3+5)x = 8x
• Subtracting like terms: Subtract the coefficients of like terms while keeping the variable the same.
  • Example: 9y - 4y = (9-4)y = 5y
• Simplifying expressions is the process of reducing an expression to its simplest form.
  • Steps:
    • Identify all like terms in the expression.
    • Add or subtract the coefficients of like terms, as appropriate.
    • Rewrite the expression with the simplified terms.
• Example:
  • Simplify 3a + 4b - 2a + 5b:
    • Combine like terms (3a - 2a) and (4b + 5b).
    • Result: (3-2)a + (4+5)b = 1a + 9b = a + 9b

Key Points

• Variable parts remain constant when adding or subtracting like terms.
• Only the coefficients are manipulated.
• Simplifying expressions helps solve equations efficiently.