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

2 min read Jun 16, 2024

Simplifying Polynomial Expressions

This article will guide you through the process of simplifying the following polynomial expression:

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

Understanding the Basics

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

Polynomial: An expression consisting of variables and constants combined using addition, subtraction, and multiplication. Each term in a polynomial is a product of a constant and one or more variables raised to non-negative integer powers.
Like terms: Terms that have the same variable(s) raised to the same power(s).
Combining like terms: The process of adding or subtracting coefficients of like terms.

Steps to Simplify

Distribute the negative sign: Since we're subtracting the second polynomial, we need to distribute the negative sign to each term inside the parentheses. This gives us:

(3x^4 + 2x^2 - 7) + (-2x^4 + x^3 - 4x^2)
Rearrange terms: It's helpful to group like terms together. This makes the simplification process easier:

(3x^4 - 2x^4) + x^3 + (2x^2 - 4x^2) - 7
Combine like terms: Combine the coefficients of the like terms:

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

Simplified Expression:

The simplified form of the polynomial expression is x^4 + x^3 - 2x^2 - 7.

Important Note: Remember that you cannot combine terms that have different variables or different exponents.