Simplify: $8888 + 888 + 88 + 8$

### Concept & Strategy The most efficient way to add a repetitive sequence of a single digit is by factoring out the common digit or using the column addition multiplication shortcut. ### Step-by-Step Solution * **Calculation:** Instead of standard addition, factor out the common number 8: $$ 8888 + 888 + 88 + 8 = 8 \times (1111 + 111 + 11 + 1) $$ * Add the sequence of ones: $$ 1111 + 111 + 11 + 1 = 1234 $$ * Multiply by the factored digit: $$ 8 \times 1234 = 9872 $$ ### Exam Strategy & Shortcut For repetitive additions of the same digit, simply multiply the digit by the descending sequence of its count. Here, 8 appears 4 times, then 3, then 2, then 1. Simply calculate $8 \times 1234 = 9872$ to get the answer in seconds. ### Common Pitfall When doing traditional column addition under time pressure, students often misalign the place values, leading to incorrect sums in the hundreds and thousands places. Always align right-to-left if writing it out. ### Final Answer Therefore, the correct answer is **9872**.