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

Jasonbradley

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Jun 17, 2024

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Simplifying Polynomial Expressions

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

Understanding the Basics

Before we begin simplifying, let's understand the key concepts:

• Polynomial: An expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, with non-negative integer exponents.
• Terms: Individual parts of a polynomial separated by addition or subtraction signs.
• Like terms: Terms with the same variable and exponent.

Step-by-Step Simplification

1. Distribute the negative sign: The minus sign in front of the second set of parentheses indicates that we need to multiply each term within the parentheses by -1: (x - 2x^3 + 8 - 7x^2) + (-1 * 8) + (-1 * 5x) + (-1 * -3x^3)

2. Simplify the expression: This gives us: x - 2x^3 + 8 - 7x^2 - 8 - 5x + 3x^3

3. Combine like terms: Group the terms with the same variables and exponents: (-2x^3 + 3x^3) + (x - 5x) + (-7x^2) + (8 - 8)

4. Simplify further: x^3 - 4x - 7x^2

Final Simplified Expression

The simplified form of the expression (x-2x^3+8-7x^2)-(8+5x-3x^3) is x^3 - 4x - 7x^2. It's important to note that the order of the terms doesn't impact the expression's value, but it's generally customary to arrange terms in descending order of their exponents.