$(71 \times 29 + 27 \times 15 + 8 \times 4)$ equals

Concept & Formula This problem requires the application of the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction). The multiplications inside the bracket must be resolved first before summing the final values. Step-by-Step Solution * The given expression is: $$(71 \times 29) + (27 \times 15) + (8 \times 4)$$ * Calculate the first product. Use $29 = 30 - 1$: $$71 \times (30 - 1) = 2130 - 71 = 2059$$ * Calculate the second product. Use $15 = 10 + 5$: $$27 \times (10 + 5) = 270 + 135 = 405$$ * Calculate the third product: $$8 \times 4 = 32$$ * Sum all the computed values: $$2059 + 405 + 32 = 2496$$ Exam Strategy & Shortcut The unit digit concept is the fastest way to crack this. Calculate only the last digit of each multiplication component: $1 \times 9 = 9$ $7 \times 5 = 35 \rightarrow 5$ $8 \times 4 = 32 \rightarrow 2$ Sum of unit digits = $9 + 5 + 2 = 16$. The final answer must end with a $6$. Looking at the options, only $2496$ ends in $6$. Common Pitfall A common error is getting bogged down in traditional multiplication for $71 \times 29$ and making arithmetic mistakes. Using the nearest multiple of ten (like $30-1$) simplifies the math drastically. Final Answer **Therefore, the correct answer is 2496.**