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

Question

UpStudy AI · Accepted Answer

To find the value of $$2011^2 - 2010^2$$, we can use the algebraic identity for the difference of squares:

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

**Step 1: Identify $$a$$ and $$b$$**
$$
a = 2011 \
b = 2010
$$

**Step 2: Apply the Difference of Squares Formula**
$$
2011^2 - 2010^2 = (2011 + 2010)(2011 - 2010)
$$

**Step 3: Simplify the Expressions Inside the Parentheses**
$$
2011 + 2010 = 4021 \
2011 - 2010 = 1
$$

**Step 4: Multiply the Results**
$$
4021 \times 1 = 4021
$$

**Final Answer:**
$$
2011^2 - 2010^2 = 4021
$$
$$2011^2 - 2010^2 = 4021$$

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