## The Distributive Property: A Fundamental Concept in Algebra

The equation **(y^2 + y)(3y^3 - 2y^3) = y^2(3y^3 - 2y^3) + y(3y^3 - 2y^3)** is a perfect example of the **distributive property** in algebra.

### Understanding the Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend of the sum by the number and then adding the products.

In simpler terms, **we can "distribute" a factor to each term inside parentheses**.

### Applying the Property to the Equation

In the given equation, we have:

**(y^2 + y)**as the sum being multiplied**(3y^3 - 2y^3)**as the factor being distributed

The equation demonstrates how the distributive property works:

**Distributing to the first term**:**y^2(3y^3 - 2y^3)****Distributing to the second term**:**y(3y^3 - 2y^3)**

This process expands the original expression, making it easier to simplify and solve.

### Importance of the Distributive Property

The distributive property is a fundamental concept in algebra, used for:

**Simplifying expressions:**Expanding expressions like the one in the example.**Solving equations:**It is often used to remove parentheses and combine like terms.**Factoring expressions:**The reverse process of the distributive property helps in factoring out common factors.

Understanding and applying the distributive property is crucial for successful algebraic manipulation and problem-solving.