Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Guerrero Davey. in South Africa
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 2011^2 - 2010^2 = 4021 \)
Solution
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The Deep Dive
To solve \( 2011^2 - 2010^2 \), you can use the difference of squares formula, which states \( a^2 - b^2 = (a - b)(a + b) \). Here, \( a = 2011 \) and \( b = 2010 \). So we have: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating each part: - \( 2011 - 2010 = 1 \) - \( 2011 + 2010 = 4021 \) Now, putting it all together: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] Thus, the answer is: \[ \boxed{4021} \]
