Those are fake news:

a^2  = ab
a^2 - b^2 = ab - b^2
(a + b)(a - b) = b(a - b)
(a + b) = b
2b = b

But, those are real:

 def foo(n):
       if n == 1:
           return 1
       else: 
           return foo(n - 1) + n + n - 1