Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Chambers Pollard. in Nigeria
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:
\[
a^2 - b^2 = (a + b)(a - b)
\]
Here, \( a = 2011 \) and \( b = 2010 \). Applying the formula:
\[
2011^2 - 2010^2 = (2011 + 2010)(2011 - 2010)
\]
Let's compute each part:
1. **Sum**: \( 2011 + 2010 = 4021 \)
2. **Difference**: \( 2011 - 2010 = 1 \)
Now, multiply the sum and the difference:
\[
4021 \times 1 = 4021
\]
**Answer:** \( 2011^2 - 2010^2 = 4021 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
Did you know there’s a nifty way to solve \( a^2 - b^2 \)? It’s called the difference of squares formula! The formula states that \( a^2 - b^2 = (a - b)(a + b) \). So, when you set \( a = 2011 \) and \( b = 2010 \), you can quickly calculate \( 2011^2 - 2010^2 \) as \( (2011 - 2010)(2011 + 2010) \). That's \( 1 \times 4021 \)! In the end, it’s super fast to get your answer: \( 2011^2 - 2010^2 = 4021 \). This method is a lifesaver for when numbers are too large to compute directly, showing just how powerful algebra can be!
