%2B(4x%5E3-9x%5E2-11x%2B1).jpeg "(3x^3+7x-1)+(4x^3-9x^2-11x+1)")
Simplifying Polynomial Expressions: (3x^3+7x-1)+(4x^3-9x^2-11x+1)
This article will guide you through the process of simplifying the polynomial expression: (3x^3+7x-1)+(4x^3-9x^2-11x+1).
Understanding the Basics
Before we begin, let's quickly review some key concepts:
- Polynomial: A mathematical expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
- Terms: Individual parts of a polynomial separated by plus or minus signs.
- Like Terms: Terms that have the same variables raised to the same powers.
Simplifying the Expression
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Identify Like Terms:
- x^3 terms: 3x^3 and 4x^3
- x^2 terms: -9x^2
- x terms: 7x and -11x
- Constant terms: -1 and 1
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Combine Like Terms:
- x^3 terms: 3x^3 + 4x^3 = 7x^3
- x^2 terms: -9x^2
- x terms: 7x - 11x = -4x
- Constant terms: -1 + 1 = 0
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Write the Simplified Expression:
Combining all the terms, we get the simplified expression: 7x^3 - 9x^2 - 4x
Conclusion
By identifying and combining like terms, we successfully simplified the given polynomial expression. The simplified form, 7x^3 - 9x^2 - 4x, is easier to work with and understand. Remember, combining like terms is a fundamental skill in algebra, and it's crucial for solving various mathematical problems.