$2056 \times 987 = x$

### Concept & Formula When a multiplier is close to a thousand (like 987), we can express it as 1000 minus a small integer to use the distributive property, significantly simplifying the math. $$a \times (b - c) = ab - ac$$ ### Step-by-Step Solution * Express 987 as $1000 - 13$: $$2056 \times 987 = 2056 \times (1000 - 13)$$ * Distribute the multiplication: $$(2056 \times 1000) - (2056 \times 13)$$ * Calculate the two parts: $$2056000 - 26728$$ * Perform the final subtraction: $$2056000 - 26728 = 2029272$$ ### Exam Strategy & Shortcut Use the last two digits to eliminate options! The last two digits of the answer will be the last two digits of $56 \times 87$. $56 \times 87 \rightarrow 56 \times (100 - 13) = 5600 - 728 = 4872$. The last two digits are 72. All options have 72! Expand to the last three digits: $056 \times 987$. $056 \times (1000 - 13) = 56000 - 728 = 55272$. The last three digits must be 272. Only options (b) and (d) end in 272. Estimate: $2000 \times 1000 = 2000000$. The exact answer will be close to this, making 2029272 the logical choice over 1923472. ### Common Pitfall Attempting a three-by-four digit standard multiplication line by line. This takes at least triple the time and introduces a high probability of simple addition errors in the final sum. ### Final Answer **Therefore, the correct answer is 2029272.**