Expanding and factorising quadratics

There are 38 NRICH Mathematical resources connected to Expanding and factorising quadratics
Always Perfect
problem
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Always perfect

Age
14 to 18
Challenge level
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Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
Square Number Surprises
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Square number surprises

Age
14 to 16
Challenge level
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There are unexpected discoveries to be made about square numbers...
Quadratic Patterns
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Quadratic patterns

Age
14 to 16
Challenge level
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Surprising numerical patterns can be explained using algebra and diagrams...

Pythagoras Perimeters
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Pythagoras perimeters

Age
14 to 16
Challenge level
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If you know the perimeter of a right angled triangle, what can you say about the area?
Hollow Squares
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Hollow squares

Age
14 to 16
Challenge level
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Which armies can be arranged in hollow square fighting formations?
Difference of Two Squares
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Difference of two squares

Age
14 to 16
Challenge level
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What is special about the difference between squares of numbers adjacent to multiples of three?
Factorising with Multilink
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Factorising with multilink

Age
14 to 16
Challenge level
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Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
Number rules - OK
problem
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Number rules - OK

Age
14 to 16
Challenge level
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Can you produce convincing arguments that a selection of statements about numbers are true?

Common Divisor
problem
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Common divisor

Age
14 to 16
Challenge level
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Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
2-Digit Square
problem
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2-digit square

Age
14 to 16
Challenge level
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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?