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(8x^3-3x^2-2x+9)-(2x^3+6x^2-x+1)

2 min read Jun 16, 2024
(8x^3-3x^2-2x+9)-(2x^3+6x^2-x+1)

Simplifying Polynomial Expressions

This article will guide you through the process of simplifying the following polynomial expression:

(8x^3 - 3x^2 - 2x + 9) - (2x^3 + 6x^2 - x + 1)

Understanding the Process

To simplify this expression, we need to perform subtraction between two polynomials. This involves the following steps:

  1. Distribute the negative sign: The minus sign in front of the second set of parentheses indicates that we need to subtract each term within the parentheses.
  2. Combine like terms: Identify terms with the same variable and exponent (e.g., x^3, x^2, x, and constant terms) and combine their coefficients.

Step-by-Step Solution

Let's break down the simplification:

  1. Distribute the negative sign:

(8x^3 - 3x^2 - 2x + 9) + (-2x^3 - 6x^2 + x - 1)

  1. Combine like terms:
  • x^3 terms: 8x^3 - 2x^3 = 6x^3
  • x^2 terms: -3x^2 - 6x^2 = -9x^2
  • x terms: -2x + x = -x
  • Constant terms: 9 - 1 = 8

Final Result

After combining like terms, the simplified expression is:

6x^3 - 9x^2 - x + 8

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