## The Distributive Property

The equation **(x⁴ + 3x³ - 2x³)(-5x² + x) = (x⁴ + 3x³ - 2x³)(-5x²) + (x⁴ + 3x³ - 2x³)(x)** is an example of the **distributive property**.

### Understanding the Distributive Property

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

**In simpler terms:**

**To multiply a sum by a number, you distribute the multiplication to each term inside the parentheses.**

### Applying the Distributive Property to the Equation

Let's break down the equation:

**(x⁴ + 3x³ - 2x³)(-5x² + x)**: This represents the multiplication of two polynomials.**(x⁴ + 3x³ - 2x³)(-5x²) + (x⁴ + 3x³ - 2x³)(x)**: This demonstrates the distributive property being applied. The first polynomial is distributed to each term in the second polynomial.

The distributive property allows us to expand and simplify expressions like this one. By applying it, we can perform the multiplications and combine like terms, ultimately arriving at a simplified expression.

### Key Takeaways

- The distributive property is a fundamental principle in algebra.
- It allows us to multiply polynomials and simplify expressions.
- The distributive property states that we can distribute multiplication over addition or subtraction.
- Understanding the distributive property is essential for solving equations and working with algebraic expressions.