$\{(476 + 424)^2 - 4 \times 476 \times 424\} = x$

### Concept & Formula This expression is a classic application of a derived algebraic identity. It represents the relationship between the square of a sum and the square of a difference. $$(a + b)^2 - 4ab = (a - b)^2$$ ### Step-by-Step Solution * Identify the core variables in the given expression: Let $a = 476$ and $b = 424$. * Substitute these variables into the structural formula: $$(476 + 424)^2 - 4(476)(424) \rightarrow (a + b)^2 - 4ab$$ * Simplify the expression into the squared difference: $$(476 - 424)^2$$ * Perform the subtraction: $$476 - 424 = 52$$ * Calculate the final square: $$(52)^2 = 2704$$ ### Exam Strategy & Shortcut To square 52 quickly, use the base-50 squaring method. For a number $(50 + x)^2$, the result is composed of two parts: $(25 + x)$ and $(x^2)$. Here, $x = 2$. First part: $25 + 2 = 27$ Second part: $2^2 = 04$ (must be two digits) Combine them: 2704. You can solve this entirely in your head! ### Common Pitfall Attempting to expand $(476 + 424)^2$ into $900^2 = 810000$ and then trying to manually subtract $4 \times 476 \times 424$. While mathematically valid, the sheer size of the numbers almost guarantees a calculation error under time pressure. ### Final Answer **Therefore, the correct answer is 2704.**