Expanding and factorising quadratics

There are 38 NRICH Mathematical resources connected to Expanding and factorising quadratics

problem

Favourite

Always perfect

Age

14 to 18

Challenge level

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

problem

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Square number surprises

Age

14 to 16

Challenge level

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

problem

Favourite

Quadratic patterns

Age

14 to 16

Challenge level

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

problem

Favourite

Pythagoras perimeters

Age

14 to 16

Challenge level

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

problem

Favourite

Hollow squares

Age

14 to 16

Challenge level

Which armies can be arranged in hollow square fighting formations?

problem

Favourite

Difference of two squares

Age

14 to 16

Challenge level

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

problem

Favourite

Factorising with multilink

Age

14 to 16

Challenge level

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

problem

Favourite

2-digit square

Age

14 to 16

Challenge level

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?

problem

Favourite

Pair products

Age

14 to 16

Challenge level

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

problem

Favourite

Always two

Age

14 to 18

Challenge level

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.

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Expanding and factorising quadratics

Always perfect

Square number surprises

Quadratic patterns

Pythagoras perimeters

Hollow squares

Difference of two squares

Factorising with multilink

2-digit square

Pair products

Always two