The Difference of 2 squares

This is a continuation of Quadratic Equations
This question is very common in GCSE papers and there is no trick to it you must just learn to recognise it

You may get a question asking

Factorise x^2 - 16
This is the difference of two squares, as you are subtracting (finding the difference between) two square numbers

You must notice that a square number cannot be negative but those in The Difference of 2 squares are.
Now this is still recognisable as a quadratic as it could be rewritten as
x^2 +/-0x - 16

This means the two numbers multiply to make 16 and add to make 0.
and as this is a square number, those numbers must be 4's
and since the 16 is negative one of the 4 must be negative and one must be positive
as 2 negatives make a positive.

So we will write it out as
(x-4)(x+4)

which multiplies out as

x times x = x^2
x times -4 = -4x
x times 4 = 4x
-4 times 4 = -16
Then x^2 -4x+4x-16
And if we tidy it up
x^2 -16 then we know we have the write answer
and if the question asks
x^2 -16=0
then just follow the example in the Quadratic Equations section