(-3p^3+5p^2-2p)+(-p^3-8p^2-15p)=

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: (-3p^3 + 5p^2 - 2p) + (-p^3 - 8p^2 - 15p)

Understanding the Process

Simplifying polynomial expressions involves combining like terms. Like terms are terms that have the same variable and the same exponent. For example, 3p² and -5p² are like terms, while 3p² and 3p³ are not.

Step-by-Step Solution

1. Remove the parentheses: Since we are adding the two polynomials, the parentheses do not affect the order of operations. We can rewrite the expression as: -3p³ + 5p² - 2p - p³ - 8p² - 15p

2. Identify like terms: Now we identify the terms that have the same variable and exponent:

   • p³ terms: -3p³ and -p³
   • p² terms: 5p² and -8p²
   • p terms: -2p and -15p

3. Combine like terms: We add the coefficients of the like terms:

   • -3p³ - p³ = -4p³
   • 5p² - 8p² = -3p²
   • -2p - 15p = -17p

4. Final Expression: Combine the simplified terms to get the final expression: -4p³ - 3p² - 17p

Conclusion

Therefore, the simplified form of the polynomial expression (-3p³ + 5p² - 2p) + (-p³ - 8p² - 15p) is -4p³ - 3p² - 17p.