Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Welch Schultz. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 2011^2 - 2010^2 = 4021 \)
Solution
To find the value of \( 2011^2 - 2010^2 \), we can use the difference of squares formula:
\[
a^2 - b^2 = (a - b)(a + b)
\]
Here, \( a = 2011 \) and \( b = 2010 \). Plugging these values into the formula:
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = (1)(4021) = 4021
\]
**Answer:** \( 4021 \)
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Simplify this solution The Deep Dive
To solve \( 2011^2 - 2010^2 \), we can use 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 the two parts: 1. \( 2011 - 2010 = 1 \) 2. \( 2011 + 2010 = 4021 \) Now, we can substitute these back into the formula: \[ 2011^2 - 2010^2 = 1 \cdot 4021 = 4021 \] Therefore, the answer is: \[ \boxed{4021} \]
