Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Jimenez French. in South Africa
Mar 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 2011^2 - 2010^2 = 4021 \)
Solution
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The Deep Dive
To find \( 2011^2 - 2010^2 \), we can use the difference of squares formula, which states: \[ a^2 - b^2 = (a - b)(a + b) \] Here, \( a = 2011 \) and \( b = 2010 \). Therefore, we can rewrite the expression as follows: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating the values: \[ 2011 - 2010 = 1 \] \[ 2011 + 2010 = 4021 \] Now substituting these values back into our expression: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] Thus, the final answer is: \[ \boxed{4021} \]
