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

Ask by Colon Morgan. in the United States
Feb 21,2025

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

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The Deep Dive

To calculate \(2011^2 - 2010^2\), we can use the difference of squares formula, which states that \(a^2 - b^2 = (a-b)(a+b)\). Here, let \(a = 2011\) and \(b = 2010\). So, we get: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating the values in the parentheses: \[ 2011 - 2010 = 1 \] \[ 2011 + 2010 = 4021 \] Now, substituting back into the formula: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] Thus, the result is: \[ \boxed{4021} \]

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