$8796 \times 223 + 8796 \times 77 = x$

### Concept & Formula This problem is designed to test your knowledge of the distributive property of multiplication. Instead of performing two large multiplications, we can factor out the common term. $$ab + ac = a(b + c)$$ ### Step-by-Step Solution * Identify the common multiplier in both terms: The number 8796 is common to both $8796 \times 223$ and $8796 \times 77$. * Apply the distributive property to factor it out: $$8796 \times (223 + 77)$$ * Perform the addition inside the parentheses: $$223 + 77 = 300$$ * Multiply the factored number by the sum: $$8796 \times 300 = 2638800$$ ### Exam Strategy & Shortcut When spotting a repeated number in an addition or subtraction string, immediately look for a base-10 sum (10, 100, 300, etc.) hiding in the other multipliers. Calculating $8796 \times 300$ only requires computing $8796 \times 3$ and appending two zeros. The unit digit of $6 \times 3$ is 18, so the answer must end in 800. Since 2638800 is not among the given options (a) through (d), the answer is "None of these". ### Common Pitfall Calculating $8796 \times 223$ and $8796 \times 77$ independently. This wastes several minutes and dramatically increases the likelihood of a basic arithmetic mistake during the final addition. ### Final Answer **Therefore, the correct answer is None of these.**