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

2 min read Jun 16, 2024

Simplifying Polynomial Expressions: A Step-by-Step Guide

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

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

Understanding the Basics

Before we dive into the simplification process, let's refresh some key concepts:

Polynomial: An expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, with non-negative integer exponents.
Terms: Individual parts of a polynomial separated by addition or subtraction signs.
Like Terms: Terms that have the same variable and exponent.

Step 1: Distributing the Negative Sign

The minus sign before the second set of parentheses indicates that we need to distribute it to each term inside:

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

Step 2: Combining Like Terms

Now, we group together the terms with the same variable and exponent:

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

Step 3: Simplifying

Perform the addition and subtraction for each group of like terms:

-2x^3 + 12x^2 - 8x + 10

The Simplified Expression

The simplified form of the original polynomial expression is -2x^3 + 12x^2 - 8x + 10.

Key Takeaways

Always remember to distribute the negative sign when simplifying expressions with parentheses.
Combine like terms by adding or subtracting their coefficients.
Simplify each group of like terms to obtain the final simplified expression.