(-7x^5+14-2x)+(10x^4+7x+5x^5)

2 min read Jun 16, 2024
(-7x^5+14-2x)+(10x^4+7x+5x^5)

Simplifying Polynomial Expressions

This article will guide you through the process of simplifying the polynomial expression: (-7x^5 + 14 - 2x) + (10x^4 + 7x + 5x^5).

Understanding the Basics

Before we begin, let's clarify some key concepts:

  • Polynomial: An expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, where the exponents of the variables are non-negative integers.
  • Terms: Individual parts of a polynomial separated by addition or subtraction.
  • Like Terms: Terms that have the same variable(s) raised to the same power(s).

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 rewrite the expression as:

    -7x^5 + 14 - 2x + 10x^4 + 7x + 5x^5

  2. Identify like terms: Group the terms with the same variables and exponents:

    (-7x^5 + 5x^5) + 10x^4 + (-2x + 7x) + 14

  3. Combine like terms: Perform the indicated operations on the coefficients of the like terms:

    -2x^5 + 10x^4 + 5x + 14

Final Result

The simplified form of the polynomial expression (-7x^5 + 14 - 2x) + (10x^4 + 7x + 5x^5) is -2x^5 + 10x^4 + 5x + 14.

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