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(4x-2x^3)+(5x^3-4x+5)

2 min read Jun 16, 2024
(4x-2x^3)+(5x^3-4x+5)

Simplifying Polynomial Expressions: (4x - 2x^3) + (5x^3 - 4x + 5)

This article will guide you through the process of simplifying the polynomial expression (4x - 2x^3) + (5x^3 - 4x + 5).

Understanding the Basics

Before we begin, let's refresh some fundamental concepts about polynomials:

  • Polynomials are expressions made up of variables and constants, combined using addition, subtraction, multiplication, and non-negative integer exponents.
  • Terms within a polynomial are separated by addition or subtraction signs.
  • Like terms have the same variable and exponent.

Simplifying the Expression

  1. Remove the parentheses: Since we are adding the two polynomials, the parentheses don't affect the order of operations.

    (4x - 2x^3) + (5x^3 - 4x + 5) = 4x - 2x^3 + 5x^3 - 4x + 5

  2. Identify like terms: Group together terms with the same variable and exponent.

    -2x^3 + 5x^3 + 4x - 4x + 5

  3. Combine like terms: Combine the coefficients of the like terms.

    3x^3 + 0 + 5 = 3x^3 + 5

Final Result

The simplified form of the expression (4x - 2x^3) + (5x^3 - 4x + 5) is 3x^3 + 5.

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