Compute $99^2+99+1$ in your head.
To square 99, I can use the identity $(a-b)^2=a^2-2ab+b^2$ with $a=100$ and $b=1$. This gives $99^2=(100-1)^2=100^2-2(100)(1)+1^2=10000-200+1=9801$. To add 99 and 1, I can simply increment the ones digit of 99 by 1 and get 100. To add 9801 and 100, I can simply add 1 to the thousands digit of 9801 and get 9901. Therefore, the final answer is 9901. 