## 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.