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

Ask by Harrington Tyler. in the United States
Feb 08,2025

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

Solución

Calculate or simplify the expression \( 2011^2 - 2010^2 \). Calculate the value by following steps: - step0: Calculate: \(2011^{2}-2010^{2}\) - step1: Calculate: \(\left(2011+2010\right)\left(2011-2010\right)\) - step2: Calculate: \(4021\times 1\) - step3: Multiply the terms: \(4021\) The result of \(2011^2 - 2010^2\) is 4021.

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Bonus Knowledge

To solve \( 2011^2 - 2010^2 \), you can use the difference of squares formula, which states that \( a^2 - b^2 = (a-b)(a+b) \). Here, let \( a = 2011 \) and \( b = 2010 \). Therefore, \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = (1)(4021) = 4021. \] So, \( 2011^2 - 2010^2 = 4021 \). Isn't it fascinating how a simple algebraic identity can simplify what seems like a complex calculation? It’s like having a secret shortcut that mathematicians carry in their back pockets! If you’re into problem-solving, learning the properties of squares, cubes, and other algebraic identities can boost your efficiency. Plus, knowing these can help you spot patterns and relationships in numbers that can save time during tests or competitive exams!

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