Let: a = b,
Then: (1) a^2 = ab,
(2) a^2 - b^2 = ab - b^2,
(3) (a + b)(a - b) = b(a - b),
(4) a + b = b,
(5) 2b = b,
(6) 2 = 1

It would seem that we have proved 2 = 1.

What is wrong here?

The problem is in line 3. The value of (a-b) is zero. Zero x any number is zero. So equation 3 results out to be 0=0. You can't do the following steps afterwards. 4/5/6. Even if you use symbols, 2 does not equal 1.

Also to allow the equation to be balanced, you need to apply the same values and operations to both sides of the equation. In #3, you have (a+b) x (a-b) on the left. On the right it's b x (a-b). The equation is NOT equal at this point. And as I mentioned before (a-b) is zero.

Do I win something?

MJ