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(y^3-7x^4y^4)+(-10x^4y^3+6y^3+4x^4y^4)-(x^4y^3+6x^4y^4)

3 min read Jun 17, 2024
(y^3-7x^4y^4)+(-10x^4y^3+6y^3+4x^4y^4)-(x^4y^3+6x^4y^4)

Simplifying Polynomial Expressions

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

(y^3 - 7x^4y^4) + (-10x^4y^3 + 6y^3 + 4x^4y^4) - (x^4y^3 + 6x^4y^4)

Understanding the Basics

Before we begin, let's understand some key concepts:

  • Polynomial: A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
  • Terms: Each part of a polynomial separated by addition or subtraction is called a term.
  • Like terms: Terms with the same variables and exponents are called like terms. For example, 3x²y and -5x²y are like terms.
  • Simplifying: Simplifying a polynomial means combining like terms to express it in its simplest form.

Simplifying the Expression

  1. Remove the parentheses: Since we are adding and subtracting polynomials, we can remove the parentheses without changing the signs of the terms.

    (y^3 - 7x^4y^4) + (-10x^4y^3 + 6y^3 + 4x^4y^4) - (x^4y^3 + 6x^4y^4) = y^3 - 7x^4y^4 - 10x^4y^3 + 6y^3 + 4x^4y^4 - x^4y^3 - 6x^4y^4

  2. Identify like terms: We need to group together terms with the same variables and exponents:

    • y^3 terms: y^3 + 6y^3
    • x^4y^4 terms: -7x^4y^4 + 4x^4y^4 - 6x^4y^4
    • x^4y^3 terms: -10x^4y^3 - x^4y^3

  3. Combine like terms: Now, we add or subtract the coefficients of the like terms:

    • y^3 terms: 7y^3
    • x^4y^4 terms: -9x^4y^4
    • x^4y^3 terms: -11x^4y^3

  4. Write the simplified expression: Finally, we combine the simplified terms:

    7y^3 - 9x^4y^4 - 11x^4y^3

Final Answer

Therefore, the simplified form of the polynomial expression (y^3 - 7x^4y^4) + (-10x^4y^3 + 6y^3 + 4x^4y^4) - (x^4y^3 + 6x^4y^4) is 7y^3 - 9x^4y^4 - 11x^4y^3.

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