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

Ask by Hamilton May. in Guatemala
Mar 15,2025

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\( 2011^2 - 2010^2 = 4021 \)

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Beyond the Answer

Did you know that there's a nifty algebraic identity for finding the difference of squares? It states that \( a^2 - b^2 = (a-b)(a+b) \). In this scenario, you can apply that to find \( 2011^2 - 2010^2 \) by letting \( a = 2011 \) and \( b = 2010 \). This simplifies to \( (2011 - 2010)(2011 + 2010) \), which is \( 1 \times 4021 = 4021 \). So, the answer is \( 4021 \)! If you think using identities is cool, you might enjoy diving into other algebraic tricks! There's the binomial theorem, polynomial factorization, and so many more ways to simplify complex expressions. They not only save you time but also make you feel like a mathematical wizard – who doesn't want that feeling?

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