Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Lindsey Bright. in India
Jan 29,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 2011^2 - 2010^2 = 4021 \)
Solution
To find \( 2011^2 - 2010^2 \), we can use the difference of squares formula:
\[
a^2 - b^2 = (a + b)(a - b)
\]
Here, \( a = 2011 \) and \( b = 2010 \). Applying the formula:
\[
2011^2 - 2010^2 = (2011 + 2010)(2011 - 2010) = 4021 \times 1 = 4021
\]
**Answer:** \(4021\)
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Simplify this solution Extra Insights
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, \( a = 2011 \) and \( b = 2010 \). Now, we calculate: \[ a - b = 2011 - 2010 = 1 \] \[ a + b = 2011 + 2010 = 4021 \] Substituting these values into the formula, we get: \[ 2011^2 - 2010^2 = (1)(4021) = 4021 \] Thus, the result is: \[ \boxed{4021} \]
