Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Reid Mccarthy. in Myanmar
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 2011^2 - 2010^2 = 4021 \)
Solution
To find \( 2011^2 - 2010^2 \), we can use the difference of squares formula:
\[
a^2 - b^2 = (a - b)(a + b)
\]
**Step 1:** Identify \( a \) and \( b \).
\[
a = 2011 \\
b = 2010
\]
**Step 2:** Apply the formula.
\[
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
\]
**Step 3:** Calculate the differences and sums.
\[
2011 - 2010 = 1 \\
2011 + 2010 = 4021
\]
**Step 4:** Multiply the results.
\[
1 \times 4021 = 4021
\]
**Answer:** \( 2011^2 - 2010^2 = \boxed{4021} \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To find \( 2011^2 - 2010^2 \), you can use the difference of squares formula, which states that \( a^2 - b^2 = (a - b)(a + b) \). Here, let \( a = 2011 \) and \( b = 2010 \). Thus, \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) = (1)(4021) = 4021. \] So, \( 2011^2 - 2010^2 = 4021 \).
