Evaluate: $986 \times 137 + 986 \times 863$

### Concept & Logic This problem relies on the Distributive Property of Multiplication over Addition. The formula is $a \times b + a \times c = a \times (b + c)$. Identifying a common factor allows you to simplify complex arithmetic into simple base-10 multiplication. ### Step-by-Step Solution * **Given:** $986 \times 137 + 986 \times 863$ * **Calculation:** Identify the common factor, which is $986$. Factor it out of the expression: $$ 986 \times (137 + 863) $$ * Simplify the addition inside the parentheses first: $$ 137 + 863 = 1000 $$ * Multiply by the factored number: $$ 986 \times 1000 = 986000 $$ ### Exam Strategy & Shortcut Scan expressions for repeating numbers before doing any math. If you see the same large number being multiplied in separate terms, always factor it out. The non-common numbers (here, $137$ and $863$) are almost always designed by the examiner to sum perfectly to $10$, $100$, or $1000$. ### Common Pitfall A strict, blind application of the BODMAS rule without looking for algebraic simplifications first will cause a student to multiply $986 \times 137$ and $986 \times 863$ separately, taking minutes instead of seconds. ### Final Answer Therefore, the correct answer is **986000**.