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 $x-4$.