What does the distributive property state?

The distributive property is a fundamental principle in algebra that describes how to distribute a multiplication operation over addition or subtraction. Specifically, it states that when you multiply a number by a sum, you can distribute the multiplication to each addend in the sum.

In the context of the question, the statement a(b + c) = ab + ac clearly illustrates this concept. On the left side, you have a product of 'a' and the sum of 'b' and 'c'. According to the distributive property, you distribute 'a' to both 'b' and 'c', resulting in the two products: 'ab' and 'ac'. Thus, the equation holds true, reaffirming the definition of the distributive property.

This principle is not only essential in simplifying expressions but also in solving equations, demonstrating its importance in various areas of mathematics. Understanding this property enables students to tackle a wide range of algebraic problems effectively.