Expanding Double Brackets

Introduction

• Expanding double brackets involves multiplying two brackets together, each containing algebraic expressions.
• Essential to multiply each term in the first bracket by each term in the second bracket.

Method Step-by-Step

1. Identify Terms

   • Start with the first term of the first bracket.
   • Multiply it by every term in the second bracket.

2. Example 1: (x + 4)(2x - 3)

   • Multiply:
     • x by 2x → 2x²
     • x by -3 → -3x
     • 4 by 2x → 8x
     • 4 by -3 → -12
   • Simplify:
     • Combine like terms: -3x + 8x = 5x
   • Result: 2x² + 5x - 12

3. Example 2: (2a - 3)(3a - 4)

   • Multiply:
     • 2a by 3a → 6a²
     • 2a by -4 → -8a
     • -3 by 3a → -9a
     • -3 by -4 → 12
   • Simplify:
     • Combine like terms: -8a - 9a = -17a
   • Result: 6a² - 17a + 12

Techniques

• Traditional Method: Works for any number of terms in brackets.
• Formal/Face Methods: May not be applicable if there are more than two terms in any bracket.

Additional Example

• For more complex brackets, use the same approach: multiply each term systematically using arrows for clarity.
• Example:
  • Multiply each term of the first bracket by each term of the second:
  • Resulting expression: 2x² + 6xA - x + 9A - 6

Conclusion

• This method is a reliable approach for expanding double brackets regardless of complexity.
• Remember to always combine like terms to simplify the expression.

Final Note

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