(3x^2+2xy+4y^2)+(6x^2-5xy+3y^2)+(9x^2-25y^2)

Jasonbradley

less than a minute read

·

Jun 16, 2024

44

Share

Simplifying Polynomial Expressions

This article explores the simplification of the following polynomial expression:

(3x² + 2xy + 4y²) + (6x² - 5xy + 3y²) + (9x² - 25y²)

Understanding the Process

Simplifying polynomial expressions involves combining like terms. Like terms are those that have the same variables raised to the same powers.

Step-by-Step Simplification

1. Identify like terms:

   • x² terms: 3x², 6x², 9x²
   • xy terms: 2xy, -5xy
   • y² terms: 4y², 3y², -25y²

2. Combine like terms by adding or subtracting their coefficients:

   • x² terms: 3x² + 6x² + 9x² = 18x²
   • xy terms: 2xy - 5xy = -3xy
   • y² terms: 4y² + 3y² - 25y² = -18y²

3. Write the simplified expression: 18x² - 3xy - 18y²

Final Result

The simplified form of the polynomial expression (3x² + 2xy + 4y²) + (6x² - 5xy + 3y²) + (9x² - 25y²) is 18x² - 3xy - 18y².