Expanding and factorising quadratics

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

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.

Can you produce convincing arguments that a selection of statements about numbers are true?

The sums of the squares of three related numbers is also a perfect square - can you explain why?

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

If you know the perimeter of a right angled triangle, what can you say about the area?

There are unexpected discoveries to be made about square numbers...

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?

What do you get when you raise a quadratic to the power of a quadratic?

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.