Expanding Triple Brackets

Overview

Expanding triple brackets involves multiplying three brackets together.
The process requires careful attention and clear presentation of workings to avoid mistakes.

Initial Multiplication:
- Ignore one bracket and multiply the other two together to form a combined bracket.
- Essentially, you're performing a double bracket expansion twice.
Final Multiplication:
- Multiply the resultant bracket from step 1 by the bracket that was initially ignored.
- This step gives you the final expanded form.

Example 1:
1. Start with three brackets: For instance, (2x + 3)(x + 2)(x + 4).
2. Ignore the last bracket initially (x + 4).
3. Multiply the first two brackets:
  - Multiply terms: 2x by x and 2, 3 by x and 2.
  - Result: 2x^2 + 4x + 3x + 6
  - Simplify to: 2x^2 + 7x + 6
4. Place the simplified bracket in brackets: (2x^2 + 7x + 6)
5. Multiply with the ignored bracket (x + 4):
  - Use distributive property:
  - For "x":
    - x * 2x^2 = 2x^3
    - x * 7x = 7x^2
    - x * 6 = 6x
  - For "4":
    - 4 * 2x^2 = 8x^2
    - 4 * 7x = 28x
    - 4 * 6 = 24
6. Combine like terms:
  - 2x^3 + (7x^2 + 8x^2) + (6x + 28x) + 24
  - Result: 2x^3 + 15x^2 + 34x + 24
Example 2:
1. Choose different brackets: (2x - 1)(x - 2)(x + 3)
2. Ignore (x + 3) and multiply (2x - 1) with (x - 2):
  - Result: 2x^2 - 4x - x + 2
  - Simplify to: 2x^2 - 5x + 2
3. Multiply with the ignored bracket (x + 3):
  - For "x": 2x^2 - 5x + 2
    - x * 2x^2 = 2x^3
    - x * -5x = -5x^2
    - x * 2 = 2x
  - For "3":
    - 3 * 2x^2 = 6x^2
    - 3 * -5x = -15x
    - 3 * 2 = 6
4. Combine like terms:
  - 2x^3 + (6x^2 - 5x^2) + (2x - 15x) + 6
  - Result: 2x^3 + x^2 - 13x + 6