Jasonbradley
Home

(x^2y+x^3-xy^2+3)+(x^3+xy^2-xy-6)

2 min read Jun 17, 2024
(x^2y+x^3-xy^2+3)+(x^3+xy^2-xy-6)

Simplifying Polynomial Expressions

This article will explore how to simplify the following polynomial expression:

(x²y + x³ - xy² + 3) + (x³ + xy² - xy - 6)

Understanding Polynomials

A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication. Each term in a polynomial is a product of a constant (coefficient) and one or more variables raised to non-negative integer powers.

Combining Like Terms

To simplify the expression, we need to combine like terms. Like terms are those that have the same variables raised to the same powers.

  1. Identify like terms:

    • x²y: The first expression has one term with x²y.
    • x³: Both expressions have terms with x³.
    • xy²: Both expressions have terms with xy².
    • xy: The second expression has one term with xy.
    • Constant terms: The first expression has a constant term of +3, and the second has a constant term of -6.

  2. Combine coefficients of like terms:

    • x²y: 1x²y + 0x²y = 1x²y
    • x³: 1x³ + 1x³ = 2x³
    • xy²: -1xy² + 1xy² = 0xy²
    • xy: 0xy - 1xy = -1xy
    • Constant terms: 3 - 6 = -3

Simplified Expression

After combining like terms, the simplified expression is:

2x³ + x²y - xy - 3

Featured Posts