Practice Problems and Variations

This page provides additional practice problems for expanding triple brackets, reinforcing the skills learned in the previous section. It includes several examples with different complexities.

1. (x+5)(x-3)(x-6) = x³-4x²-27x+90
2. (x-4)³ = x³-12x²+48x-64
3. (x-9)(x-2)(x-4) = x³-15x²+62x-72

Example: (x-4)³ is equivalent to (x-4)(x-4)(x-4), which expands to x³-12x²+48x-64.

The page also introduces a worded question involving the area of a rectangle:

Example: Find the area of a rectangle with dimensions (x+3) and (x+5). Solution: Area = (x+3)(x+5) = x²+8x+15

Additionally, it touches on the area of a triangle formula:

Vocabulary: Area of a triangle = (base × height) ÷ 2

Highlight: Practice with various types of triple brackets, including cubes like (x-4)³, is crucial for mastering this topic in GCSE maths.

These examples and practice problems provide a comprehensive approach to expanding triple brackets, preparing students for GCSE questions and worksheets on this topic.

Multiplying Out Triple Brackets

This page introduces the concept of expanding triple brackets, a fundamental skill in GCSE maths. The main example provided is (x+2)(x+3)(x-4), which is solved step-by-step to demonstrate the process.

Definition: Expanding triple brackets involves multiplying three algebraic expressions enclosed in parentheses to obtain a single polynomial expression.

The expansion process is broken down as follows:

1. First, multiply (x+2) by (x+3), resulting in x²+3x+2x+6.
2. Simplify this to x²+5x+6.
3. Then, multiply this result by (x-4).
4. Distribute each term: x³-4x², 5x²-20x, and 6x-24.
5. Combine like terms to get the final answer: x³+x²-14x-24.

Example: (x+2)(x+3)(x-4) = x³+x²-14x-24

This method can be applied to various triple brackets expansion examples in GCSE.

Highlight: Pay close attention to signs when multiplying, especially with negative terms like (x-4).