Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Harris Barrett. 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, which is a useful algebraic identity. The difference of squares states that:
\[
a^2 - b^2 = (a - b)(a + b)
\]
Applying this formula to your problem:
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
\]
Now, calculate each part:
1. **Subtract the numbers:**
\[
2011 - 2010 = 1
\]
2. **Add the numbers:**
\[
2011 + 2010 = 4021
\]
3. **Multiply the results:**
\[
1 \times 4021 = 4021
\]
So,
\[
2011^2 - 2010^2 = 4021
\]
**Answer:** \( 4021 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
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, let \( a = 2011 \) and \( b = 2010 \). Now, applying the formula: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating \( 2011 - 2010 \), we get \( 1 \), and for \( 2011 + 2010 \), we have: \[ 2011 + 2010 = 4021 \] Putting it all together: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] Thus, the answer is \( \boxed{4021} \).
