Final answer:
By using the distributive property, we can rewrite the expressions and compare them to see that both 851 × 29 and 849 × 31 yield the same product when simplified. Thus, both expressions have the same product.
Step-by-step explanation:
To determine which expression yields a bigger product, let us use the distributive property to compare 851 × 29 with 849 × 31. The distributive property allows us to rewrite these expressions in a form that makes them easier to compare. For instance, we can write both expressions as a product of two numbers that are close to each other: 851 × 29 can be written as (850 + 1) × (30 - 1), 849 × 31 can be written as (850 - 1) × (30 + 1). Looking at these rewritten forms, if we distribute the first numbers, we get 850 × 30 + 1 × 30 - 1 × 1 for the first expression and 850 × 30 - 1 × 30 + 1 × 1 for the second expression. Breaking it down, both expressions have the common term 850 × 30, and differ only in the last two terms. When we simplify, we see that the +1 × 30 and the -1 × 30 terms cancel each other out in comparison. Therefore, the expressions only really differ by 1 × 1. Thus, both expressions yield the same value. Owing to this equivalence, we can instinctively check off the correct answer: c) Both have the same product.