I don't agree with your math teacher. ⇔ is not equivalence, it's a symbol for 'if and only if'. The left hand side implies the right hand side, and vice versa.

I don't agree with your math teacher. ⇔ is not equivalence, it's a symbol for 'if and only if'. The left hand side implies the right hand side, and vice versa. Writing a * a - b * b ⇔ (a + b)(a - b) doesn't make any sense, because neither the left hand side nor the right hand side are logic statements.