-(-7x%5E4-5-9x).jpeg "(-7x-5x^4+5)-(-7x^4-5-9x)")
Simplifying Polynomial Expressions: A Step-by-Step Guide
This article will guide you through simplifying the polynomial expression (-7x - 5x⁴ + 5) - (-7x⁴ - 5 - 9x).
Understanding the Basics
Before we dive into the simplification, let's review some key concepts:
- Polynomial: An expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
- Terms: The individual parts of a polynomial separated by plus or minus signs.
- Like Terms: Terms with the same variable and exponent.
Simplifying the Expression
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Distribute the Negative Sign: We begin by distributing the negative sign in front of the second set of parentheses.
(-7x - 5x⁴ + 5) + (7x⁴ + 5 + 9x)
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Combine Like Terms: Now, identify and combine terms with the same variable and exponent:
- x⁴ terms: -5x⁴ + 7x⁴ = 2x⁴
- x terms: -7x + 9x = 2x
- Constant terms: 5 + 5 = 10
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Write the Simplified Expression: Combine the simplified terms to get the final result:
2x⁴ + 2x + 10
Conclusion
By following these steps, we have successfully simplified the given polynomial expression. Remember, the key is to distribute the negative sign and then combine like terms to arrive at the simplest form.