Jasonbradley
Home

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

2 min read Jun 16, 2024
(4x^2-5xy+3y^2)-(3x^2+2xy-y^2)

Simplifying Algebraic Expressions: (4x² - 5xy + 3y²) - (3x² + 2xy - y²)

This article will guide you through simplifying the algebraic expression: (4x² - 5xy + 3y²) - (3x² + 2xy - y²).

Understanding the Problem

We are tasked with subtracting one polynomial from another. To achieve this, we will follow the steps outlined below.

Step-by-Step Solution

  1. Distribute the Negative Sign: Remember that subtracting a polynomial is the same as adding its negative. We can rewrite the expression as:

    (4x² - 5xy + 3y²) + (-3x² - 2xy + y²)

  2. Combine Like Terms: Identify and group terms with the same variable and exponent:

    (4x² - 3x²) + (-5xy - 2xy) + (3y² + y²)

  3. Simplify: Perform the addition or subtraction for each group of like terms:

    x² - 7xy + 4y²

Final Answer

The simplified form of the expression (4x² - 5xy + 3y²) - (3x² + 2xy - y²) is x² - 7xy + 4y².

Key Takeaways

  • Distribution of Negatives: When subtracting polynomials, remember to distribute the negative sign to all terms within the parentheses.
  • Combining Like Terms: Identify terms with the same variables and exponents to simplify the expression effectively.
  • Order of Operations: Pay attention to the order of operations (PEMDAS/BODMAS) when simplifying expressions.

Related Post

Featured Posts