(3x^3+3x^2+9)-(5x^3-7x^2+6x-9)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions

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

(3x^3 + 3x^2 + 9) - (5x^3 - 7x^2 + 6x - 9)

Understanding the Problem

The expression involves two sets of polynomials enclosed in parentheses. To simplify it, we need to follow the order of operations and combine like terms.

Step-by-Step Solution

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

   (3x^3 + 3x^2 + 9) + (-5x^3 + 7x^2 - 6x + 9)

2. Combine like terms: Group together terms with the same variable and exponent:

   (3x^3 - 5x^3) + (3x^2 + 7x^2) - 6x + (9 + 9)

3. Simplify: Perform the arithmetic operations on the coefficients:

   -2x^3 + 10x^2 - 6x + 18

Final Result

The simplified form of the expression (3x^3 + 3x^2 + 9) - (5x^3 - 7x^2 + 6x - 9) is -2x^3 + 10x^2 - 6x + 18.