$(24 + 25 + 26)^2 - (10 + 20 + 25)^2 = x$

### Concept & Formula First, you must evaluate the arithmetic sums inside the parentheses, and then apply the difference of squares identity to conclude the equation efficiently. $$a^2 - b^2 = (a - b)(a + b)$$ ### Step-by-Step Solution * Calculate the sum found in the first bracket: $$24 + 25 + 26 = 75$$ * Calculate the sum found in the second bracket: $$10 + 20 + 25 = 55$$ * Substitute these evaluated sums back into the original expression: $$(75)^2 - (55)^2$$ * Apply the difference of squares formula where $a = 75$ and $b = 55$: $$(75 - 55)(75 + 55) = (20)(130)$$ * Multiply the final simplified terms: $$20 \times 130 = 2600$$ ### Exam Strategy & Shortcut Notice that $24 + 25 + 26$ is a simple arithmetic progression. Its sum is just the middle term multiplied by the number of terms ($25 \times 3 = 75$). This quickly gives you the first squared term mentally. Then, using the standard $(a-b)(a+b)$ algebraic rule transforms a complex squaring problem into basic mental math. ### Common Pitfall Squaring 75 and 55 manually ($5625 - 3025$) mathematically works but leaves immense room for basic subtraction errors under pressure. Always default to $(a-b)(a+b)$ when you naturally spot a difference of squares. ### Final Answer Therefore, the correct answer is **2600**.