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This is a quick derivation of the quadratic formula for an GCSE Maths students looking to stretch themselves a little and go for that A*!

If we have a general quadratic equation:

It is important to remember this is an estimate, so we can simplify the numbers by saying they get 20% off and the drill costs £90. (1)

10% off would be £9, so 20% off is £18. (1)<...

Step 1 - Identify the difference between the required form of the answer and the expression to be simplified: 

It can be...

(7+√5)/(√5-1) 

In this example we are given (√5-1) as our denominator, and we want to simplify this complex fraction into the form a + b√5. 

In order to do this our first st...

Expanding something out like (x+2)(x+3) crops up everywhere in maths. Therefore it's a very important skill to develop.There are many different ways of looking at it - smily faces, rainbows, claws - to na...