When you factor an expression you divide them into more parts. Say 10/2 = 5, so then 5 x 2 = 10. You would have divided 10 into two different parts, 5 and 2. They are divided into different parts so then to undo that division you would multiply them together. Multiplication is the inverse of division. That would be why when you factor an expression, they are multiplied together. This is really basic stuff, I don't know what all that other garbage proves. Zero is the only number that has zero as a factor, both sides where equal to zero, the only number that you could factor out a zero from is zero since it is the only number that has zero as a factor. Did I mention that the only number that has zero as a factor is zero? Do you know of any other numbers that can be a product of a factor of zero? Lets try 1, does 1 have a factor of zero in it? Can we factor out a zero out of 1? Lets see 1/0 = undefined darn didn't work. Lets try 2, does 2 have a factor of zero? 2/0 = undefined , How about 3 anything we could multiple by zero in order to get 3? 3/0= undefined, oh well I give up, have a nice day.