Compute $115^2$ in your head.
I know that $(a+b)^2 = a^2 + 2ab + b^2$, so I can try to write 115 as a sum of two numbers that are easy to square. One possible way is to write 115 as 100 + 15, since 100 and 15 are both easy to square. Then I can use the formula to get $(100+15)^2 = 100^2 + 2 \times 100 \times 15 + 15^2$. I know that $100^2 = 10000$, $2 \times 100 \times 15 = 3000$, and $15^2 = 225$. So adding them up, I get $10000 + 3000 + 225 = 13225$. 