Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Evans Wheeler. in India
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 2011^2 - 2010^2 = 4021 \)
Solution
Using the difference of squares formula, we have
\[
a^2 - b^2 = (a-b)(a+b)
\]
Let \( a = 2011 \) and \( b = 2010 \). Then
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
\]
Calculating the difference and the sum:
\[
2011 - 2010 = 1
\]
\[
2011 + 2010 = 4021
\]
Now multiply the two results:
\[
1 \times 4021 = 4021
\]
Thus, the value is
\[
\boxed{4021}
\]
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Simplify this solution Beyond the Answer
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, \( a = 2011 \) and \( b = 2010 \). First, calculate \( a - b \) and \( a + b \): - \( a - b = 2011 - 2010 = 1 \) - \( a + b = 2011 + 2010 = 4021 \) Now, substitute these values into the difference of squares formula: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = 1 \cdot 4021 = 4021 \] So, the answer is \( 4021 \).
