Final answer:
To determine which product is greater, we compared the largest factors in each expression. Expression (b) 269 × 5 × 7 is greater because its largest factor, 269, is much larger than the largest factor in expression (a), which is 33.
Step-by-step explanation:
The student is asked to compare two large products without actually multiplying the numbers. For the first product, 26 × 33 × 5 × 7 × 9, and the second product, 269 × 5 × 7, we can simplify the comparison by focusing on the largest factors in each product.
For the first expression (a), the largest factor is 33, and for the second expression (b), it's 269. Since each expression is composed of multiplying positive integers, we can determine which expression is greater by comparing these two largest factors. Clearly, 269 is much larger than 33, which indicates that expression (b) 269 × 5 × 7 will result in a greater product than expression (a) 26 × 33 × 5 × 7 × 9.