Important Algebra Skills

Multiplying and Simplifying Brackets

• Step 1: Multiply constants with variables inside the brackets.
  • Example: Multiply 3 with 2x to get 6x.
  • Multiply 3 by -3y to get -9y.
• Step 2: Carefully multiply each term, especially with negative signs.
  • Example: Multiply -4 with x to get -4x.
  • Multiply -4 with -2y to get +8y.
• Step 3: Simplify the result.
  • Combine like terms: 6x - 4x = 2x.
  • Combine -9y + 8y = -y.

Changing Order in Multiplication

• Example Problem: Multiply several terms.
  • Expression: 2 * 3 * a^2 * a * b * b^3 * c.
• Steps to Simplify:
  • Compute numerical multiplication: 2 * 3 = 6.
  • Use the laws of exponents: a^2 * a = a^3.
  • Compute b * b^3 = b^4.
  • Result: 6a^3b^4c.

Simplifying Division

• Convert Division to Multiplication: Write numerator and denominator as products.
• Simplification Process:
  • Example: 15a^2b^3dC divided by 3abC^3.
  • Cancel common terms: cancel out 3, a, b, and C.
  • Result: 5ab^2 / C^2.

Division of Fractions

• Strategy: Convert division into multiplication by flipping the second fraction.
  • Expression: (2a^2 / 3b^2c) ÷ (6a / 7c^3b^2).
• Steps:
  • Swap the second fraction and multiply.
  • Cancel terms directly from this form:
    • Cancel 2 with 6, simplification gives 3.
    • Cancel C with C^3, leaves C^2.
    • Cancel a with a^2, leaves a.
• Result: Simplified expression: 7aC^2 / 9b^4.

Homework

• Complete similar problems and review the simplification process for accuracy.
• Bring completed questions to the next lesson for discussion.