%2B(2x%5E3-5x%5E2-x).jpeg "(5x^3+7x-8)+(2x^3-5x^2-x)")
Simplifying Polynomial Expressions: (5x^3+7x-8)+(2x^3-5x^2-x)
This article will guide you through the process of simplifying the polynomial expression: (5x^3+7x-8)+(2x^3-5x^2-x).
Understanding the Basics
Before we dive into the simplification, let's review some fundamental concepts about polynomials:
- Polynomials: Expressions involving variables with non-negative integer exponents, combined with constants, using addition, subtraction, and multiplication.
- Terms: Individual parts of a polynomial separated by plus or minus signs.
- Like Terms: Terms that have the same variable and exponent.
Simplifying the Expression
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Remove the Parentheses: Since we're adding polynomials, the parentheses don't affect the order of operations. We can simply remove them:
(5x^3 + 7x - 8) + (2x^3 - 5x^2 - x) = 5x^3 + 7x - 8 + 2x^3 - 5x^2 - x
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Combine Like Terms: Identify and group terms with the same variable and exponent:
- x^3 terms: 5x^3 + 2x^3 = 7x^3
- x^2 terms: -5x^2
- x terms: 7x - x = 6x
- Constant terms: -8
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Write the Simplified Expression: Combine all the like terms to get the simplified expression:
7x^3 - 5x^2 + 6x - 8
Conclusion
Therefore, the simplified form of the polynomial expression (5x^3+7x-8)+(2x^3-5x^2-x) is 7x^3 - 5x^2 + 6x - 8. Remember, combining like terms is the key to simplifying polynomial expressions.