Evaluate $796 \times 796 - 204 \times 204$

### Concept & Formula The problem is formatted as the difference between two squares, $a^2 - b^2$. This is a classic algebraic structure that can be factored to eliminate the need for any actual squaring: $$ a^2 - b^2 = (a + b)(a - b) $$ ### Step-by-Step Solution * Let $a = 796$ and $b = 204$. * The expression given is $(796)^2 - (204)^2$. * Substitute the values into the difference of squares identity: $$ (796)^2 - (204)^2 = (796 + 204)(796 - 204) $$ * Calculate the sum in the first bracket: $$ 796 + 204 = 1000 $$ * Calculate the difference in the second bracket: $$ 796 - 204 = 592 $$ * Multiply the two results: $$ 1000 \times 592 = 592000 $$ ### Exam Strategy & Shortcut Never manually square large numbers when a minus sign separates them. The difference of squares is one of the most important time-saving identities in quantitative aptitude. Notice how $(796 + 204)$ cleanly adds up to $1000$—this is a deliberate design by the examiner to reward students who spot the pattern. ### Common Pitfall A common pitfall is ignoring the pattern entirely and attempting the brute-force calculation. This wastes precious minutes on a timed exam and vastly increases the likelihood of a simple arithmetic mistake. ### Final Answer Therefore, the correct answer is **592000**.