Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Burton Clarke. in the United States
Feb 03,2025
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Tutor-Verified Answer
Answer
\( 2011^2 - 2010^2 = 4021 \)
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To solve \( 2011^2 - 2010^2 \), we can utilize the difference of squares formula, which states that \( a^2 - b^2 = (a-b)(a+b) \). Here, let \( a = 2011 \) and \( b = 2010 \). Calculating the difference: \[ a - b = 2011 - 2010 = 1 \] Calculating the sum: \[ a + b = 2011 + 2010 = 4021 \] Now we can apply the difference of squares formula: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = (1)(4021) \] Thus, \[ 2011^2 - 2010^2 = 4021 \] So the answer is \( \boxed{4021} \).
