Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Fuentes Pierce. in the United States
Jan 23,2025
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:
\[
a^2 - b^2 = (a - b)(a + b)
\]
Let's apply this formula to the given numbers:
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
\]
Calculate each part:
\[
2011 - 2010 = 1
\]
\[
2011 + 2010 = 4021
\]
Now multiply the results:
\[
1 \times 4021 = 4021
\]
**Answer:** \( 4021 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To solve \( 2011^2 - 2010^2 \), you can use the difference of squares formula, which states that \( a^2 - b^2 = (a - b)(a + b) \). Here, let \( a = 2011 \) and \( b = 2010 \). First, calculate \( a - b \) and \( a + b \): \[ a - b = 2011 - 2010 = 1 \] \[ a + b = 2011 + 2010 = 4021 \] Now apply the difference of squares formula: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = 1 \times 4021 = 4021 \] Therefore, \( 2011^2 - 2010^2 = 4021 \).
