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

Question

UpStudy AI · Accepted Answer

We start with the identity for the difference of squares:

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

Here, we set $$ a = 2011 $$ and $$ b = 2010 $$. Thus,

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

Now, compute the sum and the difference:

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

Multiplying these together:

$$
4021 \times 1 = 4021
$$

Therefore,

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

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