Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Wyatt Ingram. in South Africa
Mar 16,2025
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Tutor-Verified Answer
Answer
\( 2011^2 - 2010^2 = 4021 \)
Solution
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Bonus Knowledge
To solve \(2011^2 - 2010^2\), we can use the difference of squares formula, which states that \(a^2 - b^2 = (a-b)(a+b)\). Here, we can set \(a = 2011\) and \(b = 2010\). Calculating \(a - b\) and \(a + b\): \[ a - b = 2011 - 2010 = 1 \] \[ a + b = 2011 + 2010 = 4021 \] Now, applying the difference of squares formula: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = 1 \times 4021 = 4021 \] Therefore, the result is: \[ \boxed{4021} \]
