(x^4-x^2+9)-(13-6x^2+8x)

Jasonbradley

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Jun 17, 2024

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Simplifying Polynomial Expressions

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

(x^4 - x^2 + 9) - (13 - 6x^2 + 8x)

Understanding the Expression

The expression involves two sets of parentheses. The first set contains the terms: x^4 - x^2 + 9. The second set contains the terms: 13 - 6x^2 + 8x.

The minus sign between the parentheses indicates subtraction.

Simplifying the Expression

To simplify, 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 second parentheses by -1.

   (x^4 - x^2 + 9) + (-1 * 13) + (-1 * -6x^2) + (-1 * 8x)

2. Simplify the multiplication:

   (x^4 - x^2 + 9) - 13 + 6x^2 - 8x

3. Combine like terms: Combine the terms with the same variable and exponent.

   x^4 + (-1 + 6)x^2 - 8x + (9 - 13)

4. Final simplification:

   x^4 + 5x^2 - 8x - 4

Conclusion

The simplified form of the polynomial expression (x^4 - x^2 + 9) - (13 - 6x^2 + 8x) is x^4 + 5x^2 - 8x - 4.