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(x^3+10x^2-9)-(x^3+4x^2-13x-4)

2 min read Jun 17, 2024
(x^3+10x^2-9)-(x^3+4x^2-13x-4)

Simplifying Polynomial Expressions: (x^3+10x^2-9)-(x^3+4x^2-13x-4)

This article will guide you through simplifying the polynomial expression: (x^3+10x^2-9)-(x^3+4x^2-13x-4)

Understanding the Problem

We have two polynomial expressions enclosed in parentheses and separated by a subtraction sign. Our goal is to simplify the expression by combining like terms.

Simplifying the Expression

  1. Distribute the negative sign:

    • The subtraction sign in front of the second parenthesis means we multiply each term inside the second parenthesis by -1. This gives us:

    (x^3+10x^2-9) + (-1)(x^3+4x^2-13x-4)

    (x^3+10x^2-9) -x^3 -4x^2 + 13x + 4

  2. Combine like terms:

    • Identify terms with the same variable and exponent.
    • Combine the coefficients of these terms:

    (x^3 - x^3) + (10x^2 - 4x^2) + 13x + (-9 + 4)

  3. Simplify:

    • Combine the coefficients:

    6x^2 + 13x - 5

Solution

The simplified form of the expression (x^3+10x^2-9)-(x^3+4x^2-13x-4) is 6x^2 + 13x - 5.

Key Takeaways

  • Distributing: Remember to distribute the negative sign when subtracting polynomial expressions.
  • Combining Like Terms: Combine terms with the same variable and exponent.
  • Order of Operations: Follow the order of operations (PEMDAS/BODMAS) when simplifying expressions.

By following these steps, you can successfully simplify polynomial expressions involving subtraction.

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