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There are **10** NRICH Mathematical resources connected to **Difference of two squares**, you may find related items under Algebraic expressions, equations and formulae.

Problem
Primary curriculum
Secondary curriculum
### Hollow Squares

Which armies can be arranged in hollow square fighting formations?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Difference of Two Squares

What is special about the difference between squares of numbers adjacent to multiples of three?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Why 24?

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What's Possible?

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Plus Minus

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Odd Differences

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = nÂ² Use the diagram to show that any odd number is the difference of two squares.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 2-digit Square

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Age 14 to 16

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
### DOTS Division

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Euler's Squares

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...

Age 14 to 16

Challenge Level