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

Question

UpStudy AI · Accepted Answer

We start with the expression:

$$
2011^2 - 2010^2
$$

Recognize that this is a difference of two squares, which can be factored using the identity:

$$
a^2 - b^2 = (a+b)(a-b)
$$

Let:

$$
a = 2011 \quad \text{and} \quad b = 2010
$$

Then we have:

$$
2011^2 - 2010^2 = (2011 + 2010)(2011 - 2010)
$$

Now, calculate each part:

$$
2011 + 2010 = 4021
$$

$$
2011 - 2010 = 1
$$

Multiply the factors:

$$
4021 \times 1 = 4021
$$

Thus, the answer is:

$$
\boxed{4021}
$$
The answer is 4021.

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