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(x^3-x^2+4)-(3x^3-2x^2+3)

2 min read Jun 17, 2024
(x^3-x^2+4)-(3x^3-2x^2+3)

Simplifying Polynomial Expressions: (x^3 - x^2 + 4) - (3x^3 - 2x^2 + 3)

This article will guide you through the process of simplifying the polynomial expression (x^3 - x^2 + 4) - (3x^3 - 2x^2 + 3).

Understanding the Problem

The expression involves subtracting two polynomials. We need to simplify it by combining like terms.

Step-by-Step Simplification

  1. Distribute the negative sign: The minus sign before the second set of parentheses means we multiply each term inside the second parentheses by -1.

    This gives us: x^3 - x^2 + 4 - 3x^3 + 2x^2 - 3

  2. Identify and combine like terms:

    • x^3 terms: x^3 - 3x^3 = -2x^3
    • x^2 terms: -x^2 + 2x^2 = x^2
    • Constant terms: 4 - 3 = 1

  3. Write the simplified expression: Combining the like terms gives us the final simplified expression: -2x^3 + x^2 + 1

Conclusion

Therefore, the simplified form of the expression (x^3 - x^2 + 4) - (3x^3 - 2x^2 + 3) is -2x^3 + x^2 + 1.

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