The Attempt at a Solution
This is where I get stuck.
How about: if [itex](a+1)^3 =(b+1)^3\,,[/itex] then [itex](a+1)^3-(b+1)^3=0\,.[/itex]
Then factor into difference of cubes.
I haven't taken calculus yet but would it suggestion look like this? f(x)=(x+1)^3 I've already graphed it & seen that it's 1:1 but I'm looking to do this algebraically. Excuse me if I misinterpreted your post.Do you know any calculus? That's the easy way to prove this. Show y is an always increasing function of x.