(-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 walk through the process of simplifying the expression (-3p^3+5p^2-2p)+(-p^3-8p^2-15p).

Understanding Polynomials

A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication. Each term in a polynomial consists of a coefficient and a variable raised to a non-negative integer power.

Simplifying the Expression

1. Identify Like Terms:

   • p^3 terms: -3p^3 and -p^3
   • p^2 terms: 5p^2 and -8p^2
   • p terms: -2p and -15p

2. Combine Like Terms:

   • p^3 terms: -3p^3 - p^3 = -4p^3
   • p^2 terms: 5p^2 - 8p^2 = -3p^2
   • p terms: -2p - 15p = -17p

3. Write the Simplified Expression: The simplified expression is -4p^3 - 3p^2 - 17p.

Conclusion

By identifying and combining like terms, we have successfully simplified the polynomial expression (-3p^3+5p^2-2p)+(-p^3-8p^2-15p) to -4p^3 - 3p^2 - 17p. This process is essential for solving equations, evaluating expressions, and understanding the relationships between different polynomial expressions.