Expanding Triple Brackets
Expanding Triple Brackets
GCSE Mathematics (Higher)📦 What are Triple Brackets?
Expanding triple brackets means multiplying three binomial expressions together. The process involves expanding two brackets first, then multiplying the result by the third bracket. This topic is typically for Higher GCSE students.
Example: (x + 1)(x + 2)(x + 3)
Step 1: (x + 1)(x + 2) = x² + 3x + 2
Step 2: (x² + 3x + 2)(x + 3) = x³ + 6x² + 11x + 6
Step 1: (x + 1)(x + 2) = x² + 3x + 2
Step 2: (x² + 3x + 2)(x + 3) = x³ + 6x² + 11x + 6
🔢 The Method: Step by Step
Step 1: Expand any two brackets first
Choose any two brackets to expand first using FOIL method.
(x + 1)
×
(x + 2)
=
x² + 3x + 2
Step 2: Multiply the result by the third bracket
Now multiply your quadratic by the remaining bracket.
(x² + 3x + 2)
×
(x + 3)
=
x³ + 6x² + 11x + 6
📚 Types of Triple Brackets
➕ All Brackets Positive
All terms are positive - the most straightforward type.
Example 1: (x + 1)(x + 2)(x + 3)
Example 2: (x + 2)(x + 3)(x + 4)
Example 3: (x + 1)(x + 3)(x + 5)
➖ With Negative Signs
Be careful with signs! Negative × Negative = Positive.
Example 1: (x - 1)(x + 2)(x + 3)
Example 2: (x - 2)(x + 3)(x - 4)
Example 3: (x - 1)(x - 2)(x - 3)
🔢 With Coefficients
Multiply coefficients carefully and use index laws.
Example 1: (2x + 1)(x + 2)(x + 3)
Example 2: (3x - 1)(x + 2)(2x - 3)
⬆️ Perfect Cubes
When all three brackets are the same: (x + a)³
Example 1: (x + 2)³
Example 2: (x - 1)³
🧮 Interactive Triple Bracket Expander
Enter your own triple brackets and see them expand step-by-step!
✏️ Practice Triple Brackets
Expand: (x + 1)(x + 2)(x + 3)
Correct: 0
Attempted: 0
🎯 Common Patterns to Recognize
Pattern 1: Consecutive numbers
(x + n)(x + n+1)(x + n+2)
Pattern 2: Symmetric brackets
(x + a)(x + b)(x + c) where a + b + c = constant