-(7x%5E2-6x%5E3).jpeg "(3x^5+8x^3)-(7x^2-6x^3)")
Simplifying Polynomial Expressions: (3x^5 + 8x^3) - (7x^2 - 6x^3)
This article will guide you through the process of simplifying the polynomial expression (3x^5 + 8x^3) - (7x^2 - 6x^3).
Understanding the Basics
Before we dive into simplifying, let's understand the key concepts:
- Polynomial: An expression consisting of variables and constants, combined using addition, subtraction, and multiplication.
- Terms: Individual components of a polynomial, separated by addition or subtraction.
- Like Terms: Terms that have the same variables raised to the same powers.
Simplifying the Expression
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Distribute the negative sign: The minus sign in front of the second parenthesis means we multiply each term inside by -1. This gives us: 3x^5 + 8x^3 - 7x^2 + 6x^3
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Combine like terms: Identify and combine the terms with the same variable and exponent: 3x^5 + (8x^3 + 6x^3) - 7x^2
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Simplify: Add the coefficients of the like terms: 3x^5 + 14x^3 - 7x^2
Final Result
The simplified form of the expression (3x^5 + 8x^3) - (7x^2 - 6x^3) is 3x^5 + 14x^3 - 7x^2.