Question
\[ \text{Find } 2011^2 - 2010^2 \text{?} \]
Ask by Olson Wood. in South Africa
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 2011^2 - 2010^2 = 4021 \)
Solution
Given the expression
\[
2011^2 - 2010^2,
\]
we can use the difference of squares formula:
\[
a^2 - b^2 = (a+b)(a-b).
\]
Here, let \( a = 2011 \) and \( b = 2010 \). Substituting these values, we have:
\[
2011^2 - 2010^2 = (2011 + 2010)(2011 - 2010).
\]
Now, compute each part:
\[
2011 + 2010 = 4021,
\]
\[
2011 - 2010 = 1.
\]
Therefore, the expression simplifies to:
\[
4021 \times 1 = 4021.
\]
Thus, the final answer is:
\[
4021.
\]
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Simplify this solution Extra Insights
To find \(2011^2 - 2010^2\), we can use the difference of squares formula, which is given by: \[ a^2 - b^2 = (a - b)(a + b) \] In this case, let \(a = 2011\) and \(b = 2010\). So, we have: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating each part: \[ 2011 - 2010 = 1 \] \[ 2011 + 2010 = 4021 \] Putting it all together, we get: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] Thus, the answer is: \[ \boxed{4021} \]
