(2x^3+5x-8)+(5x^3-9x^2-11x+5)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions: (2x^3+5x-8)+(5x^3-9x^2-11x+5)

In mathematics, simplifying polynomial expressions involves combining like terms to make the expression easier to understand and work with. Let's break down how to simplify the expression: (2x^3+5x-8)+(5x^3-9x^2-11x+5).

Understanding the Process

1. Identify Like Terms:
   • Like terms have the same variable and exponent. For example, 2x^3 and 5x^3 are like terms, as are 5x and -11x.
2. Combine Like Terms:
   • Add the coefficients of like terms while keeping the variables and exponents the same.

Applying the Process

Let's apply these steps to our expression:

(2x^3+5x-8)+(5x^3-9x^2-11x+5)

1. Identify Like Terms:

   • x^3 terms: 2x^3 and 5x^3
   • x^2 terms: -9x^2
   • x terms: 5x and -11x
   • Constant terms: -8 and 5

2. Combine Like Terms:

   • x^3 terms: 2x^3 + 5x^3 = 7x^3
   • x^2 terms: -9x^2
   • x terms: 5x - 11x = -6x
   • Constant terms: -8 + 5 = -3

Simplified Expression

Combining all the simplified terms, the final simplified expression is:

7x^3 - 9x^2 - 6x - 3