Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Hodges Lee. in the United States
Jan 24,2025
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. **Sum:** \( 2011 + 2010 = 4021 \)
2. **Difference:** \( 2011 - 2010 = 1 \)
Now, multiply these results:
\[
4021 \times 1 = 4021
\]
**Therefore,**
\[
2011^2 - 2010^2 = \boxed{4021}
\]
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 utilize the difference of squares formula, which states that \( a^2 - b^2 = (a-b)(a+b) \). Here, let \( a = 2011 \) and \( b = 2010 \). Calculating the difference and the sum: \[ a - b = 2011 - 2010 = 1 \] \[ a + b = 2011 + 2010 = 4021 \] Now substituting back into the formula: \[ 2011^2 - 2010^2 = (1)(4021) = 4021 \] Thus, the final answer is: \[ \boxed{4021} \]
