Factoring the first two terms, we have:

$99^2+99+1=99(99+1)+1=99\cdot 100+1=9900+1=\boxed{9901}$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Compute $99^2+99+1$ in your head.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
9901
Compute $99^2+99+1$ in your head.
test