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(y^2+y)(x^4+3x^3-2x^3)=y^2(x^4+3x^3-2x^3)+y(x^4+3x^3-2x^3) Is An Example Of

2 min read Jun 17, 2024
(y^2+y)(x^4+3x^3-2x^3)=y^2(x^4+3x^3-2x^3)+y(x^4+3x^3-2x^3) Is An Example Of

The Distributive Property in Action

The equation (y^2+y)(x^4+3x^3-2x^3)=y^2(x^4+3x^3-2x^3)+y(x^4+3x^3-2x^3) is a clear 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 of the sum by the number and then adding the products together.

In simpler terms:

  • a(b + c) = ab + ac

This property applies to both numbers and variables, making it a fundamental concept in algebra.

Applying the Distributive Property in the Equation

In the provided equation, we see the distributive property applied in two ways:

  1. Expanding the left side: The term (y^2 + y) is distributed across the expression (x^4 + 3x^3 - 2x^3).

    • y^2 is multiplied by each term inside the second parentheses.
    • y is also multiplied by each term inside the second parentheses.

  2. Simplifying the right side: The right side of the equation demonstrates the outcome of applying the distributive property on the left side.

The Importance of the Distributive Property

The distributive property is crucial for simplifying expressions and solving equations. It allows us to break down complex expressions into smaller, easier-to-manage parts. This skill is essential for working with polynomials and other algebraic concepts.

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