Given A=B, you can say that A^2=AB, which means A^2-B^2=AB-B^2, and since A^2-B^2 can be simplified to (A+B)(A-B), and AB-B^2 is simplified to B(A-B), you can say (A+B)(A-B)=B(A-B). Then, divide each side by (A-B), you get A+B=B. In other words, A+A=A, or 2A=A, or 2=1.
