Polynomials

• What is the expression being simplified in the study material?

  (@yty-by).ay.ay - 2xy - 3xy = -boxy
• What does the term @yty-by represent in the expression?

  A variable multiplied by a constant
• How is ay.ay simplified in the expression?

  It simplifies to ay²
• What is the simplified form of -2xy?

  Already simplified
• What is the simplified form of -3xy?

  Already simplified
• What does -boxy represent in the expression?

  A variable multiplied by a constant
• How do we simplify the expression (@yty-by).ay² - 5xy = -boxy?

  • Combine -2xy and -3xy to get -5xy
  • The expression becomes (@yty-by).ay² - 5xy = -boxy
• What analogy is used to explain the expression simplification?

  It's compared to a matching game with toys
• What does the term "mystery toy" refer to in the analogy?

  It refers to @yty-by and -boxy
• What is the process for subtracting expressions from each other?

  • Take the difference between like terms
  • Identify y², x², and xy terms
• What are the two expressions being subtracted?

  2y² - 4x² and 6x² - 3xy + 8y²
• How do you subtract the y² terms in the expressions?

  2y² - 8y² = -6y²
• What is the result of subtracting the x² terms?

  -4x² - 6x² = -10x²
• How do you handle the xy terms when subtracting?

  Include +3xy since there is no xy term
• What is the final result after combining the results of the subtraction?

  • The difference is $- 6y² - 10x² +$$3xy$
• What is the simplified form of the expression 2y² - 4x² - (6x² - 3xy + 8y²)?

  -6y² - 10x² + 3xy