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

Question

UpStudy AI · Accepted Answer

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

We know that for any numbers $$a$$ and $$b$$,  
$$
a^2 - b^2 = (a - b)(a + b)
$$

**Step 2: Substitute the Given Values**

Here, $$a = 2011$$ and $$b = 2010$$. Thus,  
$$
2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010)
$$

**Step 3: Compute the Differences and Sum**

Calculate the difference:  
$$
2011 - 2010 = 1
$$

Calculate the sum:  
$$
2011 + 2010 = 4021
$$

**Step 4: Multiply to Get the Final Answer**

Now, multiply these two results:  
$$
1 \times 4021 = 4021
$$

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

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