Evaluate: $983 \times 207 - 983 \times 107$

### Concept & Logic This question tests the Distributive Property of Multiplication over Subtraction, represented by the formula $a \times b - a \times c = a \times (b - c)$. By factoring out the common multiplier, you turn a tedious calculation into mental math. ### Step-by-Step Solution * **Given:** $983 \times 207 - 983 \times 107$ * **Calculation:** Extract the common multiplier, $983$: $$ 983 \times (207 - 107) $$ * Perform the subtraction inside the parentheses: $$ 207 - 107 = 100 $$ * Multiply the common factor by the result: $$ 983 \times 100 = 98300 $$ ### Exam Strategy & Shortcut Just like with addition, look for identical numbers separated by a minus sign. Factor out the $983$, and quickly subtract the remaining terms ($207 - 107 = 100$). Simply add two zeros to $983$ to arrive at the answer instantly. ### Common Pitfall Failing to spot the common factor and attempting to brute-force the multiplication of both terms individually. Examiners specifically write these numbers so that their difference is a neat power of 10 to reward students who check for patterns first. ### Final Answer Therefore, the correct answer is **98300**.