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

Question

UpStudy AI · Accepted Answer

1. Recognize the difference of squares formula:  
   $$
   a^2 - b^2 = (a - b)(a + b)
   $$

2. Let $$ a = 2011 $$ and $$ b = 2010 $$. Substitute into the formula:  
   $$
   2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
   $$

3. Evaluate each part:  
   $$
   2011 - 2010 = 1
   $$  
   $$
   2011 + 2010 = 4021
   $$

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

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

\[ \text{Find } 2011^2 - 2010^2 \text{?} \]