\[ \text{Find } 2011^2 - 2010^2 \text{?} \]

Did you know that we can solve \(2011^2 - 2010^2\) using the difference of squares formula? This nifty formula states that \(a^2 - b^2 = (a-b)(a+b)\). Here, if we let \(a = 2011\) and \(b = 2010\), we get: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = 1 \times 4021 = 4021. \] It's a great example of how math shortcuts can save time! Now, for a little bit of historical trivia, the difference of squares has been used since ancient times, notably by mathematicians in Babylon. They recognized the pattern and used it for calculations long before the formal "algebra" we know today was developed. Not only does it yield quick results, but it also showcases the timeless nature of mathematical truths!