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

To find the value of \( 2011^2 - 2010^2 \), we can use the **difference of squares** formula, which is a useful algebraic identity. Here's how you can do it step-by-step: ### Difference of Squares Formula The difference of squares states that: \[ a^2 - b^2 = (a + b)(a - b) \] This formula simplifies the calculation by breaking down the subtraction of two squares into the product of a sum and a difference. ### Applying the Formula Let's apply this formula to the given expression: \[ 2011^2 - 2010^2 \] Here, \( a = 2011 \) and \( b = 2010 \). Plugging these values into the formula gives: \[ 2011^2 - 2010^2 = (2011 + 2010)(2011 - 2010) \] ### Calculating the Terms 1. **Sum of the numbers:** \[ 2011 + 2010 = 4021 \] 2. **Difference of the numbers:** \[ 2011 - 2010 = 1 \] ### Final Calculation Now, multiply the sum and the difference: \[ 4021 \times 1 = 4021 \] ### Conclusion Therefore, \[ 2011^2 - 2010^2 = \boxed{4021} \]