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(3x^2-4x+8)+(-x^2-2x-8)

2 min read Jun 16, 2024
(3x^2-4x+8)+(-x^2-2x-8)

Simplifying Polynomial Expressions: (3x^2 - 4x + 8) + (-x^2 - 2x - 8)

This article will guide you through the process of simplifying the polynomial expression: (3x^2 - 4x + 8) + (-x^2 - 2x - 8).

Understanding the Concepts

Before we begin, let's quickly review some essential concepts:

  • Polynomials: These are expressions consisting of variables and constants combined using addition, subtraction, and multiplication.
  • Like Terms: Terms that have the same variable and exponent. For example, 3x^2 and -x^2 are like terms, while 3x^2 and 3x are not.
  • Combining Like Terms: We can simplify polynomials by combining like terms. This involves adding or subtracting their coefficients.

Simplifying the Expression

  1. Rewrite the expression: (3x^2 - 4x + 8) + (-x^2 - 2x - 8)

  2. Remove parentheses: 3x^2 - 4x + 8 - x^2 - 2x - 8

  3. Identify like terms:

    • x^2 terms: 3x^2 and -x^2
    • x terms: -4x and -2x
    • Constant terms: 8 and -8

  4. Combine like terms: (3x^2 - x^2) + (-4x - 2x) + (8 - 8)

  5. Simplify: 2x^2 - 6x

Conclusion

Therefore, the simplified form of the expression (3x^2 - 4x + 8) + (-x^2 - 2x - 8) is 2x^2 - 6x.

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