Question

How do I expand this equation: \[(1+t+t^2)^5\]
I formed the equation into a binomial equation this way: \[(1+t+t^2)^5=\sum \binom{5}{r_1}\binom{5-r_1}{r_2}t^{r_2}t^{2r_1}\]

But I have no idea how to continue from here to solve for the \[r_1\] and \[r_2\] terms from here and then to expand it.

Thanks for any help given!