Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Pena Malone. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(2011^2 - 2010^2 = 4021\)
Solution
To calculate \(2011^2 - 2010^2\), we can use the **difference of squares** formula:
\[
a^2 - b^2 = (a + b)(a - b)
\]
Let's apply this formula with \(a = 2011\) and \(b = 2010\):
\[
2011^2 - 2010^2 = (2011 + 2010)(2011 - 2010)
\]
Evaluate the expressions inside the parentheses:
\[
= (4021)(1) = 4021
\]
**Answer:** \(4021\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To find \( 2011^2 - 2010^2 \), we can use the difference of squares formula, which states that \( a^2 - b^2 = (a-b)(a+b) \). Here, we have: - \( a = 2011 \) - \( b = 2010 \) So we can calculate: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] \[ = 1 \times (2011 + 2010) \] \[ = 1 \times 4021 \] \[ = 4021 \] Thus, \( 2011^2 - 2010^2 = 4021 \).
