446²+2-446*554+554²

To simplify the expression \( 446^2 + 2 - 446 \times 554 + 554^2 \), we can look for a way to simplify it systematically. We notice that \( 446^2 + 554^2 - 446 \times 554 \) can be rearranged and expressed in a different form. The expression resembles the expansion of the square of a binomial: \[ (a - b)^2 = a^2 - 2ab + b^2 \] Let's set \( a = 554 \) and \( b = 446 \). Therefore, we can express \( -446 \times 554 \) as: \[ - \frac{1}{2}(446 \times 554) \text{ only if we have } 2ab \text{ coefficient, otherwise we need to adjust} \] However, before proceeding, let's compute the specific values: 1. Calculate \( 446^2 \): \[ 446^2 = 198916 \] 2. Calculate \( 554^2 \): \[ 554^2 = 307716 \] 3. Calculate \( 446 \times 554 \): \[ 446 \times 554 = 247084 \] Now, plugging these values into the expression: \[ 446^2 + 2 - 446 \times 554 + 554^2 = 198916 + 2 - 247084 + 307716 \] Combine the numbers step-by-step: 1. Compute \( 198916 + 307716 = 506632 \). 2. Subtract \( 247084 \) from \( 506632 \): \[ 506632 - 247084 = 259548 \] 3. Finally, add \( 2 \): \[ 259548 + 2 = 259550 \] Thus, the final result is: \[ \boxed{259550} \]