-(x%5E-3-%2B2x%5E-2--x-3).jpeg "(6x^ 2 +8x-2)-(x^ 3 +2x^ 2 -x-3)")
Simplifying Polynomial Expressions: A Step-by-Step Guide
This article will guide you through the process of simplifying the following polynomial expression:
(6x² + 8x - 2) - (x³ + 2x² - x - 3)
Understanding the Basics
Before we begin, let's refresh some key concepts:
- Polynomials: Expressions consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
- Terms: Individual components of a polynomial separated by + or - signs.
- Like Terms: Terms that share the same variable and exponent.
Simplifying the Expression
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Distribute the Negative Sign: The subtraction sign before the second set of parentheses implies multiplication by -1. Distribute this negative sign:
(6x² + 8x - 2) -1(x³ + 2x² - x - 3)
This becomes:
6x² + 8x - 2 - x³ - 2x² + x + 3
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Combine Like Terms: Now, identify and combine terms with the same variable and exponent:
-x³ + (6x² - 2x²) + (8x + x) + (-2 + 3)
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Simplify: Combine the coefficients of the like terms:
-x³ + 4x² + 9x + 1
Final Result
The simplified form of the expression (6x² + 8x - 2) - (x³ + 2x² - x - 3) is -x³ + 4x² + 9x + 1.
Key Takeaways:
- Remember to distribute the negative sign when subtracting polynomials.
- Combine like terms to simplify the expression.
- Always pay attention to the signs of the coefficients.