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

Question

UpStudy AI · Accepted Answer

1. Recognize that the expression is a difference of squares:
   $$
   a^2 - b^2 = (a - b)(a + b)
   $$
   
2. Let $$ a = 2011 $$ and $$ b = 2010 $$.

3. Substitute the values into the formula:
   $$
   2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
   $$

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

5. Multiply the results:
   $$
   (1)(4021) = 4021
   $$

The final answer is $$ 4021 $$.
$$ 2011^2 - 2010^2 = 4021 $$

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