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(3x^5-9)-(11+13x^2-x^4)-(10x^2+x^4)

2 min read Jun 16, 2024
(3x^5-9)-(11+13x^2-x^4)-(10x^2+x^4)

Simplifying Polynomial Expressions

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

(3x^5 - 9) - (11 + 13x^2 - x^4) - (10x^2 + x^4)

Understanding the Steps

The key to simplifying this expression lies in understanding the following:

  1. Distributing the Negative Sign: Remember that a minus sign in front of parentheses means we multiply each term inside the parentheses by -1.
  2. Combining Like Terms: We can only add or subtract terms that have the same variable and exponent.

The Simplification Process

  1. Distribute the negative signs:

    (3x^5 - 9) - (11 + 13x^2 - x^4) - (10x^2 + x^4)
    = 3x^5 - 9 - 11 - 13x^2 + x^4 - 10x^2 - x^4

  2. Combine like terms:

    = 3x^5 + (x^4 - x^4) + (-13x^2 - 10x^2) + (-9 - 11)

  3. Simplify:

    = 3x^5 - 23x^2 - 20

Final Answer

Therefore, the simplified form of the expression (3x^5 - 9) - (11 + 13x^2 - x^4) - (10x^2 + x^4) is 3x^5 - 23x^2 - 20.

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