What principle does the distributive property convey?

The distributive property is a fundamental principle in algebra that expresses how multiplication interacts with addition. The property states that when you multiply a number by a sum, you can distribute the multiplication across each addend inside the parentheses. This is clearly illustrated in the correct answer, which shows that multiplying a by the sum of b and c results in the same value as multiplying a by b and then adding that to the product of a and c.

In practical terms, if you have a specific value for a and a sum (b + c), the distributive property allows you to handle those calculations in a step-by-step, manageable way. It demonstrates that grouping addends differently does not change the outcome of their multiplication, emphasizing the relationship between addition and multiplication in mathematics.

Other options might illustrate different algebraic concepts, but they do not specifically represent the principle of the distributive property in its cleanest form as the correct answer does. Thus, the provided answer effectively encapsulates the essence of this important mathematical rule.