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

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UpStudy AI · Accepted Answer

1. Recognize that the expression $$ 2011^2 - 2010^2 $$ is a difference of squares, which can be written as  
   $$
   a^2 - b^2 = (a-b)(a+b)
   $$
   where $$ a = 2011 $$ and $$ b = 2010 $$.

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

3. Calculate the differences and sums:
   $$
   2011 - 2010 = 1
   $$
   $$
   2011 + 2010 = 4021
   $$

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

Thus, the value of $$ 2011^2 - 2010^2 $$ is $$ 4021 $$.
$$ 2011^2 - 2010^2 = 4021 $$

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