(-5x^3+2x-1)+(5x^3-5x^2-x+5)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions

In algebra, simplifying polynomial expressions involves combining like terms to create a more concise and understandable form. Let's take a look at the expression (-5x^3 + 2x - 1) + (5x^3 - 5x^2 - x + 5) and break down the process of simplification.

Understanding the Steps

1. Identify like terms: Like terms have the same variables raised to the same power. In our example, we have the following pairs of like terms:

   • -5x^3 and 5x^3
   • 2x and -x
   • -1 and 5

2. Combine like terms: Add or subtract the coefficients of the like terms while keeping the variables and exponents the same.

Performing the Simplification

Let's apply the steps to our expression:

• (-5x^3 + 5x^3) + (2x - x) + (-1 + 5)

• 0 + x + 4

The Simplified Expression

The simplified form of the expression (-5x^3 + 2x - 1) + (5x^3 - 5x^2 - x + 5) is x + 4.

Conclusion

Simplifying polynomial expressions involves combining like terms. By following the steps of identifying and combining like terms, we can simplify complex expressions into a more manageable and understandable form. This skill is essential in algebra and other mathematical disciplines where polynomial expressions are commonly used.