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

Question

UpStudy AI · Accepted Answer

We start with the expression:

$$
2011^2 - 2010^2
$$

This is a difference of two squares. Recall the algebraic identity:

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

Here, let $$a = 2011$$ and $$b = 2010$$. Substituting these into the identity gives:

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

Now, calculate the two factors:

1. $$2011 + 2010 = 4021$$
2. $$2011 - 2010 = 1$$

Multiplying these together:

$$
4021 \times 1 = 4021
$$

Thus, the final answer is:

$$
\boxed{4021}
$$
$$ 2011^2 - 2010^2 = 4021 $$

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