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

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UpStudy AI · Accepted Answer

1. We start with the expression:
   $$
   2011^2 - 2010^2
   $$

2. Recognize that this is a difference of two squares. The difference of squares formula is:
   $$
   a^2 - b^2 = (a - b)(a + b)
   $$
   Here, we set $$ a = 2011 $$ and $$ b = 2010 $$.

3. Apply the formula:
   $$
   2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
   $$

4. Simplify the expression:
   $$
   2011 - 2010 = 1
   $$
   $$
   2011 + 2010 = 4021
   $$

5. Multiply the results:
   $$
   1 \times 4021 = 4021
   $$

Thus, the final answer is:
$$
4021
$$
$$ 2011^2 - 2010^2 = 4021 $$

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