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.

This quiz covers the addition and subtraction of like terms in algebraic expressions. Learn how to identify like terms, add or subtract their coefficients, and simplify expressions to their simplest form. Perfect for reinforcing your understanding of algebraic principles.