Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Turnbull Weaver. in South Africa
Feb 03,2025
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:
\[
a^2 - b^2 = (a + b)(a - b)
\]
**Where:**
- \( a = 2011 \)
- \( b = 2010 \)
**Applying the formula:**
\[
2011^2 - 2010^2 = (2011 + 2010)(2011 - 2010)
\]
\[
= (4021)(1)
\]
\[
= 4021
\]
**Therefore,**
\[
2011^2 - 2010^2 = 4021
\]
Reviewed and approved by the UpStudy tutoring team
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Bonus Knowledge
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 \( b = 2010 \): \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010). \] Calculating each part: \[ 2011 - 2010 = 1, \] \[ 2011 + 2010 = 4021. \] Now, substituting back into the equation: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021. \] Thus, the answer is \( \boxed{4021} \).