Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Potter Rodriquez. in the United States
Mar 12,2025
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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 use the algebraic identity for the difference of squares, which states that: \[ a^2 - b^2 = (a - b)(a + b) \] Here, let \(a = 2011\) and \(b = 2010\). Plugging in the values: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating the terms in the parentheses: \[ 2011 - 2010 = 1 \] \[ 2011 + 2010 = 4021 \] Now substituting back into the equation: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] Thus, the final answer is \[ \boxed{4021} \]
