Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Horton Pena. in the United States
Jan 25,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(2011^2 - 2010^2 = 4021\)
Solution
To find the value of \(2011^2 - 2010^2\), you can use the **difference of squares** formula. The difference of squares states that:
\[
a^2 - b^2 = (a - b)(a + b)
\]
Let's apply this formula to your problem:
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
\]
Now, calculate each part:
1. **Compute \(2011 - 2010\):**
\[
2011 - 2010 = 1
\]
2. **Compute \(2011 + 2010\):**
\[
2011 + 2010 = 4021
\]
3. **Multiply the results:**
\[
(2011 - 2010)(2011 + 2010) = 1 \times 4021 = 4021
\]
**Therefore,**
\[
2011^2 - 2010^2 = 4021
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find \( 2011^2 - 2010^2 \), we can apply the difference of squares formula, which states that \( a^2 - b^2 = (a - b)(a + b) \). Here, let \( a = 2011 \) and \( b = 2010 \). So we have: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating the factors: \[ 2011 - 2010 = 1 \] \[ 2011 + 2010 = 4021 \] Now, substituting these into the equation gives: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] Thus, the result is: \[ \boxed{4021} \]
