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

To find the value of \( 2011^2 - 2010^2 \), we can use the **difference of squares** formula, which is a useful algebraic identity. The difference of squares states that: \[ a^2 - b^2 = (a - b)(a + b) \] Applying this formula to your problem: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Now, calculate each part: 1. **Subtract the numbers:** \[ 2011 - 2010 = 1 \] 2. **Add the numbers:** \[ 2011 + 2010 = 4021 \] 3. **Multiply the results:** \[ 1 \times 4021 = 4021 \] So, \[ 2011^2 - 2010^2 = 4021 \] **Answer:** \( 4021 \)