Quote: Originally Posted by

**Thorsen**
Wrong:** (a+b)(a-b)=a(a-b)** (Equation 4)

Correct: **(a+b)(a-b)= a^2-ab+ab-b^2 = a^2-b^2**

Another Edit: This is done in many forms to try and prove that **1=0**, but it is at this point that I always see this failure.

Likewise, the formula "**(a+b)(a-b)= " **deontes, that there are two answers to the formula in that there are two possible outcomes **a+b** and **a-b**... thus two different answers for this fomula either subracting **b **or adding **b. a **will never yeild the same result unless **b=0**

I don't quite understand the last paragraph... Are you saying that the two terms in (a+b)(a-b) = ???? can only mean two roots? If so, there are many polynomials with a single root. Or more properly I guess two identical roots.

Actually Equation 4 is correct

*if* a=b... The biggest error comes in the following step.

if a=b then a-b=0 and equation 5 is derived by dividing both sides by zero, which is not defined.

Of course if a=b, equation 4 can be reduced to 0=0 which is perfectly valid, but applying undefined functions makes the proof invalid.