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(-11x^4-x^3-3x^2+10x-2)-(-11x^4+5x^2-7x+13)

2 min read Jun 16, 2024
(-11x^4-x^3-3x^2+10x-2)-(-11x^4+5x^2-7x+13)

Simplifying Polynomial Expressions

This article will guide you through the process of simplifying the following polynomial expression:

(-11x^4 - x^3 - 3x^2 + 10x - 2) - (-11x^4 + 5x^2 - 7x + 13)

Understanding the Process

To simplify this expression, we will follow these steps:

  1. 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.
  2. Combine like terms: We group together terms with the same variable and exponent.

Step-by-Step Solution

  1. Distribute the negative sign: (-11x^4 - x^3 - 3x^2 + 10x - 2) + 11x^4 - 5x^2 + 7x - 13

  2. Combine like terms: -x^3 + (-3x^2 - 5x^2) + (10x + 7x) + (-2 - 13)

  3. Simplify: -x^3 - 8x^2 + 17x - 15

Final Answer

The simplified form of the expression (-11x^4 - x^3 - 3x^2 + 10x - 2) - (-11x^4 + 5x^2 - 7x + 13) is -x^3 - 8x^2 + 17x - 15.

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