(-9+2x^7-x)+(9+x-2x^7)

2 min read Jun 16, 2024

Simplifying Polynomial Expressions: A Step-by-Step Guide

This article will guide you through the process of simplifying the polynomial expression (-9 + 2x^7 - x) + (9 + x - 2x^7).

Understanding the Basics

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

Polynomial: An expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
Terms: Individual parts of a polynomial separated by addition or subtraction.
Like Terms: Terms with the same variable and exponent.
Combining Like Terms: The process of adding or subtracting like terms to simplify an expression.

Simplifying the Expression

Identify Like Terms: In our expression, we have the following like terms:
- 2x^7 and -2x^7
- -x and x
- -9 and 9
Combine Like Terms:
- 2x^7 - 2x^7 = 0
- -x + x = 0
- -9 + 9 = 0
Write the Simplified Expression: After combining all the like terms, we are left with 0.

Final Result

Therefore, the simplified form of the polynomial expression (-9 + 2x^7 - x) + (9 + x - 2x^7) is 0.

Key Takeaways

Simplifying polynomial expressions involves identifying and combining like terms. This process leads to a more concise and manageable representation of the expression. In this particular case, we found that the expression simplified to zero.