2011^2 - 2010^2=

To solve \( 2011^2 - 2010^2 \), we can utilize the difference of squares formula, which states that \( a^2 - b^2 = (a-b)(a+b) \). Here, let \( a = 2011 \) and \( b = 2010 \). Thus, we have: \[ 2011^2 - 2010^2 = (2011 - 2010)(2011 + 2010) \] Calculating the expressions in the parentheses: \[ 2011 - 2010 = 1 \] \[ 2011 + 2010 = 4021 \] Now, substituting these values back into our equation: \[ 2011^2 - 2010^2 = 1 \times 4021 = 4021 \] So, the answer is: \[ \boxed{4021} \]