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(5x^3+7x-8)+(2x^3-5x^2-x+3)

2 min read Jun 16, 2024
(5x^3+7x-8)+(2x^3-5x^2-x+3)

Simplifying Polynomial Expressions: (5x^3 + 7x - 8) + (2x^3 - 5x^2 - x + 3)

This article will guide you through the process of simplifying the expression (5x^3 + 7x - 8) + (2x^3 - 5x^2 - x + 3).

Understanding the Basics

  • Polynomials: Expressions consisting of variables and constants combined using addition, subtraction, and multiplication.
  • Terms: Parts of a polynomial separated by addition or subtraction.
  • Like Terms: Terms with the same variable and exponent.

Simplifying the Expression

  1. Remove the parentheses: Since we are adding the two polynomials, the parentheses are not necessary.

    5x^3 + 7x - 8 + 2x^3 - 5x^2 - x + 3

  2. Rearrange the terms: Group like terms together for easier combination.

    5x^3 + 2x^3 - 5x^2 + 7x - x - 8 + 3

  3. Combine like terms: Add or subtract the coefficients of like terms.

    (5 + 2)x^3 - 5x^2 + (7 - 1)x + (-8 + 3)

  4. Simplify:

    7x^3 - 5x^2 + 6x - 5

Final Result

The simplified form of the expression (5x^3 + 7x - 8) + (2x^3 - 5x^2 - x + 3) is 7x^3 - 5x^2 + 6x - 5.

Key Takeaways

  • Combine like terms: The key to simplifying polynomials is to identify and combine terms with the same variables and exponents.
  • Order matters: While the order of terms doesn't affect the final result, organizing them by descending exponents (highest to lowest) is generally considered good practice.

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