1. Multiplying three brackets
This PowerPoint presentation demonstrates how to multiply out three brackets “in your head”, without going through the step of multiplying out two of the brackets first.
This is a method for those who are confident with algebraic manipulation. If it seems too hard now, stick with a method that suits you.
However, you might like to come back to this and try it again later in your course!

2. Multiplying three brackets
You need to multiply one term from each bracket, to include every possible combination.
(x – 2)(2x + 3)(3x – 1)

3. Multiplying three brackets
This is really an extension of the FOIL method for two brackets. Start by multiplying the First in the first two brackets and the first in the last bracket
(x – 2)(2x + 3)(3x – 1)
= 6x³

4. Multiplying three brackets
Next, stay with the First in the first two brackets and multiply by the second in the last bracket
(x – 2)(2x + 3)(3x – 1)
= 6x³
- 2x²

5. Multiplying three brackets
Next, multiply the Outer in the first two brackets, and multiply by the first term in the last bracket
(x – 2)(2x + 3)(3x – 1)
= 6x³
- 2x²
+ 9x²

6. Multiplying three brackets
Next, multiply the Outer in the first two brackets, and multiply by the first term in the last bracket
… and then by the second term in the last bracket
(x – 2)(2x + 3)(3x – 1)
= 6x³
- 2x²
+ 9x²
- 3x

7. Multiplying three brackets
Next, multiply the Inner in the first two brackets, and multiply by the first term in the last bracket
(x – 2)(2x + 3)(3x – 1)
- 3x
= 6x³
- 2x²
+ 9x²
- 12x²

8. Multiplying three brackets
Next, multiply the Inner in the first two brackets, and multiply by the first term in the last bracket
… and then by the second term in the last bracket
(x – 2)(2x + 3)(3x – 1)
- 12x²
- 3x
= 6x³
- 2x²
+ 9x²
+ 4x

9. Multiplying three brackets
Finally, multiply the Last in the first two brackets, and multiply by the first term in the last bracket
(x – 2)(2x + 3)(3x – 1)
+ 4x
- 12x²
- 3x
= 6x³
- 2x²
+ 9x²
- 18x

10. Multiplying three brackets
Next, multiply the Last in the first two brackets, and multiply by the first term in the last bracket
… and then by the second term in the last bracket
(x – 2)(2x + 3)(3x – 1)
- 18x
+ 4x
- 12x²
- 3x
= 6x³
- 2x²
+ 9x²
+ 6

11. Multiplying three brackets
Simplify by collecting like terms.
(x – 2)(2x + 3)(3x – 1)
+ 6
- 18x
+ 4x
- 12x²
- 3x
= 6x³
- 2x²
+ 9x²
= 6x³ - 5x² - 17x + 6