What does "$\to$" mean in "$a^3+b^3=(a+b)^3\rightarrow ab(a+b)=0$"? I'm working on this problem and I'm having difficulty understanding the solution. In the solution, it states $a^3+b^3=(a+b)^3\rightarrow ab(a+b)=0$. What do these equations mean? It doesn't seem to fit the identity $a^3+b^3=(a+b)(a^2-ab+b^2)$ if the arrow meant subtracting.

I know that right arrows can define a function, but I don't see how $(a+b)^3\rightarrow ab(a+b)=0$ could be a function. If it is, then I don't know how it is applicable to the problem, in which case it would be great if someone could explain the rest of the solution.

P.
S. I don't see this as asking two questions if that's not allowed. One is just a prerequisite to the other.
Assume that
$$
a^3  + b^3  = \left( {a + b} \right)^3 
$$
Since
$$
\left( {a + b} \right)^3  = a^3  + b^3  + 3a^2 b + 3ab^2 
$$
it follows that
$$
3a^2 b + 3ab^2  = 0
$$
thus
$$
3ab\left( {a + b} \right) = 0
$$
so that
$$
ab\left( {a + b} \right) = 0
$$
the arrow means it follows:  just calculate (a+b)^3 and subtract a^3+b^3
 what remains is 0