Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Hanson Marsh. 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:
\[
a^2 - b^2 = (a - b)(a + b)
\]
Here, \( a = 2011 \) and \( b = 2010 \). Applying the formula:
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
\]
Calculate each part:
\[
2011 - 2010 = 1
\]
\[
2011 + 2010 = 4021
\]
Now multiply them together:
\[
1 \times 4021 = 4021
\]
**Answer:** \( 4021 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
The expression \(2011^2 - 2010^2\) is a difference of squares, which can be factored using the formula \(a^2 - b^2 = (a - b)(a + b)\). Here, let \(a = 2011\) and \(b = 2010\). So, we have: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = (1)(4021) = 4021. \] Thus, \(2011^2 - 2010^2 = 4021\).
