Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Sandoval Cox. 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:
\[
a^2 - b^2 = (a + b)(a - b)
\]
**Step-by-Step Solution:**
1. **Identify \( a \) and \( b \):**
\[
a = 2011 \\
b = 2010
\]
2. **Apply the difference of squares formula:**
\[
2011^2 - 2010^2 = (2011 + 2010)(2011 - 2010)
\]
3. **Calculate the sums and differences inside the parentheses:**
\[
2011 + 2010 = 4021 \\
2011 - 2010 = 1
\]
4. **Multiply the results:**
\[
4021 \times 1 = 4021
\]
**Final Answer:**
\[
2011^2 - 2010^2 = 4021
\]
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 \(b = 2010\). Applying the formula: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating \(2011 - 2010\) gives us \(1\), and \(2011 + 2010\) gives us \(4021\). So we have: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] Thus, the solution is \(4021\).
