Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Phillips Barrett. in Kenya
Jan 27,2025
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 \( b = 2010 \). Applying the formula:
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
\]
Calculate each part:
1. **Difference:** \( 2011 - 2010 = 1 \)
2. **Sum:** \( 2011 + 2010 = 4021 \)
Now, multiply the two results:
\[
1 \times 4021 = 4021
\]
**Answer:** \( 2011^2 - 2010^2 = 4021 \)
Reviewed and approved by the UpStudy tutoring team
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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 \( a^2 - b^2 = (a - b)(a + b) \). In this case, let \( a = 2011 \) and \( b = 2010 \). Then: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = 1 \times 4021 = 4021. \] So, \( 2011^2 - 2010^2 = 4021 \).
