$$ \text{Find } 2011^2 - 2010^2 \text{?} $$

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UpStudy AI · Accepted Answer

Let's solve the problem step by step.

1. We start with the expression:
   $$
   2011^2 - 2010^2
   $$
   
2. Recognize that this is a difference of two squares, which can be factored using the identity:
   $$
   a^2 - b^2 = (a - b)(a + b)
   $$
   Here, $$a = 2011$$ and $$b = 2010$$.

3. Substitute the values into the identity:
   $$
   2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
   $$
   
4. Calculate the difference:
   $$
   2011 - 2010 = 1
   $$
   
5. Calculate the sum:
   $$
   2011 + 2010 = 4021
   $$
   
6. Multiply the difference and the sum:
   $$
   1 \times 4021 = 4021
   $$
   
Thus, the result is:
$$
\boxed{4021}
$$
The result is 4021.

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