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

Question

UpStudy AI · Accepted Answer

### Step 1: Apply the Difference of Squares Formula

The difference of squares formula is

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

Here, let $$ a = 2011 $$ and $$ b = 2010 $$.

### Step 2: Substitute the Values into the Formula

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

### Step 3: Simplify the Expression

Calculate the difference and the sum:

$$
2011 - 2010 = 1
$$

$$
2011 + 2010 = 4021
$$

Thus,

$$
2011^2 - 2010^2 = 1 \times 4021 = 4021
$$

### Final Answer

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

Upstudy AI Solution