problem: Compute the square of 989 without a calculator.
solution: \[989^2=(10^3-11)^2=10^6-2\cdot11\cdot10^3+121.\]We can factor out $10^3$ from the first two terms to make the computation easier: \[989^2=10^3(10^3-22)+121=10^3\cdot978+121=\boxed{978121}.\]