-(x%5E2%2B4x-9).jpeg "(2x^3-6x^2+1)-(x^2+4x-9)")
Simplifying Polynomial Expressions: (2x^3-6x^2+1)-(x^2+4x-9)
This article will guide you through the steps of simplifying the polynomial expression: (2x^3-6x^2+1)-(x^2+4x-9).
Understanding the Problem
The expression involves two sets of polynomials enclosed in parentheses. We need to simplify it by combining like terms.
Steps to Simplify
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Distribute the negative sign: The minus sign before the second set of parentheses means we multiply each term inside the second parentheses by -1.
(2x^3 - 6x^2 + 1) + (-1 * x^2) + (-1 * 4x) + (-1 * -9)
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Simplify the expression:
(2x^3 - 6x^2 + 1) - x^2 - 4x + 9
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Combine like terms: Identify terms with the same variable and exponent and add their coefficients.
2x^3 - 6x^2 - x^2 - 4x + 1 + 9
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Final simplification:
2x^3 - 7x^2 - 4x + 10
Conclusion
The simplified form of the polynomial expression (2x^3-6x^2+1)-(x^2+4x-9) is 2x^3 - 7x^2 - 4x + 10. This process demonstrates the key steps in combining polynomial expressions, which is a fundamental concept in algebra.