Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Lynch Lindsey. 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:
\[
a^2 - b^2 = (a + b)(a - b)
\]
**Applying the formula:**
\[
2011^2 - 2010^2 = (2011 + 2010)(2011 - 2010)
\]
\[
= (4021)(1)
\]
\[
= 4021
\]
**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 \(a^2 - b^2 = (a-b)(a+b)\). Here, we have \(a = 2011\) and \(b = 2010\). Now, applying the formula: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating each part: \[ 2011 - 2010 = 1 \] \[ 2011 + 2010 = 4021 \] Now substituting back into the formula: \[ 2011^2 - 2010^2 = 1 \cdot 4021 = 4021 \] Thus, the answer is \(4021\).
