Proof that Math is screwed up..

(a+b) (a-b) = (a*a-b*b)
=> (a+a) (a-a) = (a*a-a*a)
=> (a+a) (a-a) = a (a-a)
=> (a+a) = a(a-a) / (a-a)
=> a+a = a
=> 2a = 1a
=> 2 = 1

1=2 !!
Doesn't this mean everything we studied in Math is wrong??