(3x^4+9x^3-7x+15)+(-6x^4-8x^2+5x-3)

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:

(3x^4 + 9x^3 - 7x + 15) + (-6x^4 - 8x^2 + 5x - 3)

Before we dive into the simplification, let's review some fundamental concepts:

Polynomial: A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, with non-negative integer exponents.
Terms: Each part of a polynomial separated by addition or subtraction is called a term. For example, in the expression 3x^4 + 9x^3 - 7x + 15, there are four terms: 3x^4, 9x^3, -7x, and 15.
Like Terms: Terms with the same variables raised to the same exponents are called like terms. For instance, 3x^2 and -5x^2 are like terms, while 3x^2 and 3x are not.

To simplify the given expression, we follow these steps:

Identify like terms:
- x^4 terms: 3x^4 and -6x^4
- x^3 terms: 9x^3
- x^2 terms: -8x^2
- x terms: -7x and 5x
- Constant terms: 15 and -3
Combine like terms:
- (3x^4 - 6x^4) + 9x^3 - 8x^2 + (-7x + 5x) + (15 - 3)
Simplify:
- -3x^4 + 9x^3 - 8x^2 - 2x + 12

The simplified form of the expression (3x^4 + 9x^3 - 7x + 15) + (-6x^4 - 8x^2 + 5x - 3) is -3x^4 + 9x^3 - 8x^2 - 2x + 12.