$587 \times 999 = x$

### Concept & Formula When multiplying by 99, 999, 9999, etc., use the distributive property over subtraction. Express the multiplier as a power of 10 minus 1. $$a \times (10^n - 1) = a \times 10^n - a$$ ### Step-by-Step Solution * Express 999 as $1000 - 1$: $$587 \times 999 = 587 \times (1000 - 1)$$ * Distribute the 587: $$(587 \times 1000) - (587 \times 1)$$ $$587000 - 587$$ * Perform the subtraction: $$587000 - 587 = 586413$$ ### Exam Strategy & Shortcut When multiplying any number by a sequence of 9s (where the number of digits matches or is less), subtract 1 from the number to get the first part of the answer, and then find the 9's complement for each digit of that result to get the second part. 1. $587 - 1 = 586$ (First part) 2. $9 - 5 = 4$, $9 - 8 = 1$, $9 - 6 = 3$ (Second part: 413) Combine them: 586413. ### Common Pitfall A common mistake is misaligning the place values during subtraction (e.g., subtracting 587 from 58700 instead of 587000), leading to off-by-one place value errors. ### Final Answer **Therefore, the correct answer is 586413.**