Board Thread:Fun and Games/@comment-48285-20151005173825/@comment-1220514-20160504232845

If it was a2-b2 then you could factor to (a+b)(a-b), but since y is a dependant variable, and in this case is equivalent to x, you're trying to factor 0 [x2-x2 = 0] into 0(0) [(x-x)(x+x) = 0(0) = 0] which is nonsensical and not actually factoring. You can "factor" 0 into 0(a2+2ab+b2) since that still equals 0, but really, it isn't mathematical at all to do this.

Also I did end up googling it and this page says the factoring is the part that's wrong: http://www.curiouser.co.uk/paradoxes/1=2sol.htm You can actually cancel out variables that technically would be dividing by zero, as I said, but in this instance you can't even get to that stage.

Prince said you can't divide both sides by (x-y) since that's equivalent to zero, which is correct, but since the term is common to both sides you can cancel it out. Though in this case since it's not possible to get there it doesn't matter.