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(13xy-6y^2)+(14x^4-3y^2+x^2y^2)-(-9y^2-4xy)

2 min read Jun 16, 2024
(13xy-6y^2)+(14x^4-3y^2+x^2y^2)-(-9y^2-4xy)

Simplifying Polynomial Expressions

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

(13xy - 6y^2) + (14x^4 - 3y^2 + x^2y^2) - (-9y^2 - 4xy)

Understanding the Process

Simplifying polynomial expressions involves combining like terms. Like terms are terms that have the same variables raised to the same powers. For example, 3xy and -5xy are like terms, while 3xy and 3x^2y are not.

Step-by-Step Simplification

  1. Remove the parentheses: Since we are adding and subtracting polynomials, we can simply remove the parentheses:

    13xy - 6y^2 + 14x^4 - 3y^2 + x^2y^2 + 9y^2 + 4xy

  2. Identify like terms: Identify the terms with the same variables and powers:

    • xy terms: 13xy + 4xy
    • y^2 terms: -6y^2 - 3y^2 + 9y^2
    • x^2y^2 term: x^2y^2
    • x^4 term: 14x^4

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

    • xy terms: 13xy + 4xy = 17xy
    • y^2 terms: -6y^2 - 3y^2 + 9y^2 = 0
    • x^2y^2 term: x^2y^2 = x^2y^2
    • x^4 term: 14x^4 = 14x^4

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

    14x^4 + x^2y^2 + 17xy

Final Answer

Therefore, the simplified form of the given polynomial expression is 14x^4 + x^2y^2 + 17xy.

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