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

Question

UpStudy AI · Accepted Answer

We start with the expression

$$
2011^2 - 2010^2.
$$

Recognize that this is a difference of squares and can be factored using the identity

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

where in our case $$a = 2011$$ and $$b = 2010$$.

Substitute these values into the formula:

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

Compute the difference:

$$
2011 - 2010 = 1,
$$

and the sum:

$$
2011 + 2010 = 4021.
$$

Now, multiply the results:

$$
(1)(4021) = 4021.
$$

Thus, the final result is

$$
4021.
$$
$$ 2011^2 - 2010^2 = 4021 $$

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