If we have a = b then a^2 = ab a^2 – b^2 = ab – b^2 (a + b) (a – b) = b (a – b) a + b = b 2b = b as a=b 2 = 1 Which Law of Maths is violated if any ?

My Alg II teacher taught me the same basic thing in 11th grade: x=1 x*x=x*1 x^2=x x^2-1=x-1 (x+1)(x-1)=(x-1) x+1=1 1+1=1 2=1 same thing, different variables

For one more such fallacy, using Complex Numbers , see http://www.math.toronto.edu/mathnet/falseProofs/second1eq2.html.