Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Hardy Bob. in the United States
Jan 29,2025
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 the differences and sums:
\[
2011 - 2010 = 1
\]
\[
2011 + 2010 = 4021
\]
Now, multiply the results:
\[
1 \times 4021 = 4021
\]
**Answer:** \( 4021 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
Did you know there's a nifty algebraic identity that makes calculating the difference of squares super easy? It's expressed as \( a^2 - b^2 = (a - b)(a + b) \). For your problem, you can let \( a = 2011 \) and \( b = 2010 \). So, \( 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \). Simplifying gives you \( 1 \times 4021 = 4021 \). If you ever come across similar problems, this formula can save you time! You can replace any two numbers with their squares, and you'll always be able to calculate the difference quickly. Just remember, this works for all numbers, so add it to your problem-solving toolkit!
