Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Wang Lane. in the United States
Jan 22,2025
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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 \( b = 2010 \). So, we have: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating inside the parentheses: \[ 2011 - 2010 = 1 \] \[ 2011 + 2010 = 4021 \] Now, substitute these values back into the formula: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] Thus, the result is \[ \boxed{4021} \]
