How to factorise quadratic equations?

When factorising quadratics there's a special order that will always make it a lot easier!

First, Outside, Inside, Last! 


This is what I still use to remember how to multiply out brackets. 

If we start with an easy example and follow the FOIL method:

(x + 1)(x - 1)

First: x*x = x2

Outside: -1*x = -x

Inside: 1*x = x

Last: -1*1 = -1


Now, we have the results for each of our letters of FOIL. We take these answers and put them together in one line, by adding them all together.


x2+ (-x) + x + (-1)

If we look at this equation we can see that x squared is alone so can remain. However (-x) + x results in a value of 0 therefore we remove both of these xs as they have now cancelled each other out. 

As we pay attention to signs we see that we have (-1). If we are using addition on towards a negative number the addition is then replaced with subtraction.


Therefore our final result will be


x- 1.

Lydia B. GCSE Maths tutor, A Level Maths tutor

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