Expanding and factorising quadratics

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

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

Surprising numerical patterns can be explained using algebra and diagrams...

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

Which armies can be arranged in hollow square fighting formations?

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

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Can you find the hidden factors which multiply together to produce each quadratic expression?

Can you prove our inequality holds for all values of x and y between 0 and 1?

Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.