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(2x^2+2x-4)+(x^2+3x+7)

2 min read Jun 16, 2024
(2x^2+2x-4)+(x^2+3x+7)

Simplifying Polynomial Expressions: (2x^2 + 2x - 4) + (x^2 + 3x + 7)

This article will walk through the steps of simplifying the expression (2x^2 + 2x - 4) + (x^2 + 3x + 7).

Understanding the Concepts

To simplify this expression, we need to understand a few key concepts:

  • Polynomial: An expression consisting of variables and constants combined using addition, subtraction, and multiplication.
  • Terms: Parts of a polynomial separated by addition or subtraction signs. For example, in the expression 2x^2 + 2x - 4, the terms are 2x^2, 2x, and -4.
  • Like Terms: Terms with the same variable and exponent. For example, 2x^2 and x^2 are like terms, but 2x^2 and 2x are not.

Simplifying the Expression

  1. Remove the parentheses: Since we are adding the polynomials, we can remove the parentheses without changing the signs of the terms:

    2x^2 + 2x - 4 + x^2 + 3x + 7

  2. Combine like terms: Identify the like terms and add their coefficients.

    2x^2 + x^2 + 2x + 3x + -4 + 7

  3. Simplify:

    3x^2 + 5x + 3

Final Result

Therefore, the simplified form of the expression (2x^2 + 2x - 4) + (x^2 + 3x + 7) is 3x^2 + 5x + 3.

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