Compute $55^2 - 45^2$ in your head.
I notice that this problem involves the difference of two squares, which can be factored using the formula $(a^2 - b^2) = (a + b)(a - b)$. In this case, $a = 55$ and $b = 45$, so I can rewrite the expression as $(55 + 45)(55 - 45)$. This simplifies to $(100)(10)$, which is just 1000.

