Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Rojas Stuart. in South Africa
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(2011^2 - 2010^2 = 4021\).
Solution
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Beyond the Answer
To solve for \(2011^2 - 2010^2\), we can utilize the difference of squares formula, which states that \(a^2 - b^2 = (a - b)(a + b)\). In this case, let \(a = 2011\) and \(b = 2010\). Thus, we have: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating each part: 1. \(2011 - 2010 = 1\) 2. \(2011 + 2010 = 4021\) Now we can substitute back into the formula: \[ 2011^2 - 2010^2 = 1 \cdot 4021 = 4021 \] Therefore, the answer is \(\boxed{4021}\).
