%2B(x%5E3%2Bxy%5E2-xy-6).jpeg "(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.
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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.
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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