The puzzle for this issue involves incorrect algebra. Each of the following is a bogus algebraic rule. None of them are correct in general. The puzzle is to determine if there are any values of the variables involved for which the incorrect rule turns out to be true, and if so to find them. For example (x+y)^2 = x^2+y^2 is incorrect in general (try x=1 and y=2 if you doubt this). However, if either x or y equals 0 then it does work (and those are the only values for which it will be true). For each algebraic mistake below find all integer values of the variables involved for which the equation will be satisfied (if any exist). Include with each answer an explanation that shows how you know that there are no values besides the ones you provide that will also work. (x+y)^3 = x^3 + y^3 (x^3+y)/(x^5) = (1+y)/(x^2) 1/(x+y) = 1/x +1/y a^(x+y) = a^x + a^y