Your siggy has an error: It says:
but here's where the error is...
Where is says "(A + B)(A - B) = B(A - B)" it should not become "(A + B) = B" but rather "(A + B)(0) = B(A-B)" and according to basic math, anything time zero is zero. Therefore, B=0, and since A=B, A=0. The problem works out perfectly fine. XD Geez I feel like a nerd for figuring that out but hey, blame my teachers. XD