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(6x^2-x-8)+(-x^2-8x+12)

2 min read Jun 16, 2024
(6x^2-x-8)+(-x^2-8x+12)

Simplifying Polynomials: (6x^2-x-8) + (-x^2-8x+12)

This article will guide you through the process of simplifying the polynomial expression: (6x^2-x-8) + (-x^2-8x+12).

Understanding the Basics

Before we begin, let's refresh our understanding of some key concepts:

  • Polynomials: Expressions made up of variables and constants, combined using addition, subtraction, multiplication, and non-negative integer exponents.
  • Terms: Individual parts of a polynomial separated by addition or subtraction.
  • Like Terms: Terms that share 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. We can simply rewrite the expression as:

    6x^2 - x - 8 - x^2 - 8x + 12

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

    (6x^2 - x^2) + (-x - 8x) + (-8 + 12)

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

    5x^2 - 9x + 4

Final Result

The simplified form of the polynomial expression (6x^2-x-8) + (-x^2-8x+12) is 5x^2 - 9x + 4.

Key Takeaways

  • Simplifying polynomials involves combining like terms.
  • Remember to pay attention to the signs of the coefficients when combining terms.
  • Practice simplifying expressions to build your skills and understanding.

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