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30 April (Primary), 1 May (Secondary)

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There are **6** NRICH Mathematical resources connected to **Identities**, you may find related items under Algebraic expressions, equations and formulae.

Problem
Primary curriculum
Secondary curriculum
### Cubes Within Cubes Revisited

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Partitioning Revisited

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

Age 11 to 14

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Proofs with Pictures

Some diagrammatic 'proofs' of algebraic identities and inequalities.

Age 14 to 18

Problem
Primary curriculum
Secondary curriculum
### Binomial

By considering powers of (1+x), show that the sum of the squares of the binomial coefficients from 0 to n is 2nCn

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Particularly General

By proving these particular identities, prove the existence of general cases.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Powerful Factors

Use the fact that: x²-y² = (x-y)(x+y) and x³+y³ = (x+y) (x²-xy+y²) to find the highest power of 2 and the highest power of 3 which divide 5^{36}-1.

Age 16 to 18

Challenge Level