(y^2+y)(3y^3-2y^3)=y^2(3y^3-2y^3)+y(3y^3-2y^3) Is An Example Of

2 min read Jun 17, 2024
(y^2+y)(3y^3-2y^3)=y^2(3y^3-2y^3)+y(3y^3-2y^3) Is An Example Of

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:

  1. Distributing to the first term: y^2(3y^3 - 2y^3)
  2. 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.