Before you do this, you need to know the following:
(a+b) (a-b) = a²- b<sup>2


Here's why.
(a+b) (a-b) = a+b (a-b)
                  = a (a-b) + b (a-b)
                  =</sup> a^{2 - ab + ba -} b^{2
                
                        =}  a^{2 -} b<sup>2


Therefore:
a2 - b2 = (a+b) (a-b)</sup>

Okay, let's start.
1.   Get two numbers that are the same.   Call them a and b.
 a = b

2.   Multiply by a
a<sup>2 = ba


3.   Subtract</sup> b^{2
a2 -  b2 = ba -} b<sup>2


4.  Swap the left side with (a+b) (a-b) and factorise the right side.
(a+b) (a-b) = b (a-b)


5.   Divide by (a-b)
(a+b) = b


6.    Open brackets.
a+b = b


7.   Subtract b from both sides.
a = 0


NOTE: You cannot divide by (a-b) because a-b = 0.   You cannot divide by 0, which it why it cannot be true.


Discovered by Richard</sup>