(2x^2y^2)(4xy^5z^3)(-3x^5y^10z^18)

3 min read Jun 16, 2024
(2x^2y^2)(4xy^5z^3)(-3x^5y^10z^18)

Simplifying Polynomial Expressions: A Step-by-Step Guide

This article will guide you through the process of simplifying the polynomial expression: (2x²y²)(4xy⁵z³)(-3x⁵y¹⁰z¹⁸).

Understanding the Basics

Before we dive into the simplification, let's clarify some fundamental concepts:

  • Monomials: A monomial is a single term that can be a constant, a variable, or a product of constants and variables. For example, 2x², 4xy⁵z³, and -3x⁵y¹⁰z¹⁸ are all monomials.
  • Coefficients: The numerical factor in a monomial is called the coefficient. In our example, the coefficients are 2, 4, and -3.
  • Exponents: The exponents indicate how many times a variable is multiplied by itself. For instance, x² means x multiplied by itself twice (x * x).

Simplifying the Expression

  1. Rearrange the terms: We can rearrange the terms in the expression without changing the result. Let's group together the coefficients and the variables with the same base:

    (2 * 4 * -3) (x² * x * x⁵) (y² * y⁵ * y¹⁰) (z³ * z¹⁸)

  2. Multiply the coefficients: Multiply the numerical coefficients:

    -24 (x² * x * x⁵) (y² * y⁵ * y¹⁰) (z³ * z¹⁸)

  3. Apply the product of powers rule: When multiplying exponents with the same base, add the powers:

    -24x⁸y¹⁷z²¹

Final Result

The simplified form of the expression (2x²y²)(4xy⁵z³)(-3x⁵y¹⁰z¹⁸) is -24x⁸y¹⁷z²¹.

Key Points

  • Always remember the order of operations (PEMDAS/BODMAS).
  • Be mindful of signs (positive and negative).
  • Use the product of powers rule correctly when multiplying exponents with the same base.
  • The final answer should be written in its simplest form with no redundant operations.

Related Post


Featured Posts