**Distributive Property:**

The distributive property is a fundamental concept in mathematics that helps us simplify expressions and solve equations. It states that when we multiply a number by the sum of two or more numbers, we can multiply each number individually and then add the products together. In other words, it allows us to distribute the multiplication over addition.

**Explaining the Distributive Property:**

To better understand the distributive property, let's consider an example:

Suppose we have the expression: 3 * (2 + 4)

Using the distributive property, we can distribute the multiplication over addition as follows:

3 * (2 + 4) = (3 * 2) + (3 * 4)

Now, let's simplify each of the multiplications:

(3 * 2) = 6
(3 * 4) = 12

Finally, we add the products together:

6 + 12 = 18

Therefore, 3 * (2 + 4) = 18.

**Benefits of the Distributive Property:**

The distributive property allows us to simplify complex expressions and equations by breaking them down into simpler components. It helps us perform calculations more efficiently and accurately.

**Applications of the Distributive Property:**

The distributive property is used in various mathematical operations, such as:

1. Simplifying expressions: It allows us to simplify expressions by distributing the multiplication over addition or subtraction.

2. Solving equations: It helps us solve equations by simplifying them step by step.

3. Factoring: The distributive property can also be used in reverse to factor out common factors from expressions.

4. Algebraic manipulations: It is used extensively in algebraic manipulations to simplify equations and expressions.

**Conclusion:**

The distributive property is a powerful mathematical concept that allows us to simplify expressions and solve equations more effectively. By distributing the multiplication over addition or subtraction, we can break down complex calculations into simpler steps. Understanding and applying the distributive property is essential for success in mathematics, as it forms the foundation for various mathematical operations and problem-solving techniques.