(x^4-6x^4y-x^2y^4)-(2x^4y-2x^2y^4-6)

Jasonbradley

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Jun 17, 2024

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Simplifying Polynomial Expressions

This article will guide you through the process of simplifying the polynomial expression:

(x⁴ - 6x⁴y - x²y⁴) - (2x⁴y - 2x²y⁴ - 6)

Understanding the Problem

The expression involves multiple terms with variables (x and y) raised to different powers. We need to simplify it by combining like terms.

Steps for Simplification

1. Distribute the negative sign: The minus sign in front of the second set of parentheses means we multiply each term inside the parentheses by -1:

   (x⁴ - 6x⁴y - x²y⁴) + (-2x⁴y + 2x²y⁴ + 6)

2. Identify like terms: Look for terms with the same variables raised to the same powers.

   • x⁴ terms: x⁴ and -2x⁴y
   • x⁴y terms: -6x⁴y
   • x²y⁴ terms: -x²y⁴ and 2x²y⁴
   • Constant term: 6

3. Combine like terms: Add or subtract the coefficients of each set of like terms:

   • x⁴ terms: x⁴ - 2x⁴y = x⁴ - 2x⁴y
   • x⁴y terms: -6x⁴y = -6x⁴y
   • x²y⁴ terms: -x²y⁴ + 2x²y⁴ = x²y⁴
   • Constant term: 6 = 6

4. Write the simplified expression: Combine the simplified terms:

   x⁴ - 2x⁴y - 6x⁴y + x²y⁴ + 6

5. Combine remaining like terms: Combine the x⁴y terms:

   x⁴ - 8x⁴y + x²y⁴ + 6

Final Result

The simplified form of the polynomial expression (x⁴ - 6x⁴y - x²y⁴) - (2x⁴y - 2x²y⁴ - 6) is x⁴ - 8x⁴y + x²y⁴ + 6.