What does the distributive property state?

The distributive property is a fundamental principle in algebra that describes how to multiply a single term by a sum or difference of terms. The correct representation of this property states that when you multiply a term by a quantity inside parentheses, you distribute the multiplication across each term in the parentheses.

Specifically, the formula a(b + c) = ab + ac illustrates that you take the term 'a' and multiply it individually by both 'b' and 'c'. This ensures that the multiplication is applied to each part of the sum, resulting in the addition of the products ab and ac. This property is essential in simplifying expressions and solving equations, as it enables you to eliminate parentheses and combine like terms effectively.

The other options incorrectly represent the distributive property; they either subtract instead of adding or incorrectly apply the multiplication in various ways that do not adhere to the standard mathematical definition of distribution. Therefore, understanding and correctly applying this property is critical for success in algebra.