-(2x%5E4%2Bx%5E2-10).jpeg "(3x^5-2x^4-5)-(2x^4+x^2-10)")
Simplifying Polynomial Expressions: A Step-by-Step Guide
This article will guide you through simplifying the polynomial expression: (3x⁵ - 2x⁴ - 5) - (2x⁴ + x² - 10)
Understanding the Problem
We have two polynomials enclosed in parentheses, and we need to subtract the second polynomial from the first.
Simplifying the Expression
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Distribute the negative sign: The minus sign in front of the second set of parentheses means we multiply each term inside the parentheses by -1.
(3x⁵ - 2x⁴ - 5) + (-1)(2x⁴ + x² - 10)
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Simplify by removing the parentheses:
3x⁵ - 2x⁴ - 5 - 2x⁴ - x² + 10
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Combine like terms: Combine terms with the same variable and exponent.
3x⁵ - 4x⁴ - x² + 5
Final Result
The simplified form of the given polynomial expression is 3x⁵ - 4x⁴ - x² + 5.
Key Points to Remember
- When subtracting polynomials, distribute the negative sign to each term in the second polynomial.
- Combine like terms by adding or subtracting their coefficients.
By following these steps, you can simplify any polynomial expression involving addition or subtraction.