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

2 min read Jun 16, 2024
(5x^3+3x^2+5)-(7x^3-9x^2+8x-5)

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.

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