Use the simplification rules to calculate the following by hand.

1. [[$9^2$]]
2. [[$11^2$]]
3. [[$99^2$]]
4. [[$101^2$]]
5. [[$105^2$]]
6. [[$1001^2$]]
7. [[$999^2$]]
8. Find the pattern in the sequence [[$9^2$]], [[$99^2$]], [[$999^2$]], ...
9. Find the pattern in the sequence [[$1^2$]], [[$11^2$]], [[$101^2$]], ...