Five questions. No timer, no registration. Keep a notebook nearby and show your working. This is a small practice snapshot, not a full assessment or rank prediction.
The identity (a + b)² = a² + 2ab + b² includes a middle term. Expanding as (a + b)(a + b) gives a² + ab + ab + b².
Worked example: Expand (x + 3)².
Write (x + 3)(x + 3).
Multiply each term: x² + 3x + 3x + 9.
Combine like terms: x² + 6x + 9.
Your turn
Write your method before opening the answer. These original questions are for practice, not official past-exam papers.
1. Factorise x² − 9.
Show answer & explanation
(x − 3)(x + 3)
Use the difference-of-squares identity a² − b² = (a − b)(a + b), with a = x and b = 3.
2. Find the area of a triangle with base 12 cm and height 5 cm.
Show answer & explanation
30 cm²
Area = (1/2) × base × perpendicular height = (1/2) × 12 × 5 = 30 cm².
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