Spot the Formula!
Recognise and apply standard algebraic identities — difference of squares, square of a sum/difference, sum and difference of cubes, and Sophie Germain — to simplify expressions, prove divisibility, and evaluate products.
Start solving
Pick a puzzle below — each one has an interactive simulator you can play right away.
The problems in this set all look different on the surface — large numbers, nested radicals, telescoping products — but each one hides a standard algebraic identity waiting to be recognised.
Learn the methodRead guide
Spot the Formula!
The problems in this set all look different on the surface — large numbers, nested radicals, telescoping products — but each one hides a standard algebraic identity waiting to be recognised.
Key identities to keep in mind
| Identity | Formula |
|---|---|
| Difference of squares | |
| Square of a sum | |
| Square of a difference | |
| Sum of cubes | |
| Difference of cubes | |
| Product of four consecutive integers |
How to use this page
The problems are split into two sections.
Problems for Discussion (AID-D01 to AID-D03) are meant to be worked through with a teacher or study group. They introduce the core pattern-spotting skill.
Problems for Independent Solving (AID-S01 to AID-S07) are ordered roughly by difficulty. Try each one on your own before looking at hints.
The unifying strategy: rewrite the expression so that a known identity applies, then simplify.