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(-9xy^3-9x^4y^3)+(3xy^3+7y^4-8x^4y^4)+(3x^4y^3+2xy^3)

2 min read Jun 16, 2024
(-9xy^3-9x^4y^3)+(3xy^3+7y^4-8x^4y^4)+(3x^4y^3+2xy^3)

Simplifying Polynomial Expressions

In mathematics, simplifying polynomial expressions involves combining like terms to create a more concise and manageable form. Let's consider the following expression:

(-9xy^3 - 9x^4y^3) + (3xy^3 + 7y^4 - 8x^4y^4) + (3x^4y^3 + 2xy^3)

To simplify this expression, we'll follow these steps:

  1. Identify Like Terms: Like terms have the same variables and exponents. In this expression, we have the following groups of like terms:

    • xy^3 terms: -9xy^3, 3xy^3, 2xy^3
    • x^4y^3 terms: -9x^4y^3, 3x^4y^3
    • x^4y^4 terms: -8x^4y^4
    • y^4 terms: 7y^4

  2. Combine Like Terms: Add the coefficients of the like terms while keeping the variables and exponents the same.

    • xy^3 terms: -9xy^3 + 3xy^3 + 2xy^3 = -4xy^3
    • x^4y^3 terms: -9x^4y^3 + 3x^4y^3 = -6x^4y^3
    • x^4y^4 terms: -8x^4y^4
    • y^4 terms: 7y^4

  3. Write the Simplified Expression: Combine the simplified terms in any order.

    -4xy^3 - 6x^4y^3 - 8x^4y^4 + 7y^4

Therefore, the simplified form of the expression (-9xy^3 - 9x^4y^3) + (3xy^3 + 7y^4 - 8x^4y^4) + (3x^4y^3 + 2xy^3) is -4xy^3 - 6x^4y^3 - 8x^4y^4 + 7y^4.

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