(4x^3+2x^2-x+1)-(3x^3+2x-5)

Jasonbradley

2 min read

·

Jun 16, 2024

27

Share

Simplifying Polynomial Expressions: (4x^3+2x^2-x+1)-(3x^3+2x-5)

This article will walk you through the process of simplifying the polynomial expression: (4x^3+2x^2-x+1)-(3x^3+2x-5).

Understanding the Basics

Before we begin, let's recap some key concepts:

• Polynomials: Expressions consisting of variables and constants combined using addition, subtraction, and multiplication.
• Terms: Parts of a polynomial separated by addition or subtraction.
• Like terms: Terms that have the same variable(s) raised to the same powers.

The Steps to Simplify

1. Distribute the negative sign: The minus sign before the second parenthesis means we multiply each term inside that parenthesis by -1.

   (4x^3+2x^2-x+1) + (-1)(3x^3+2x-5)

2. Simplify the multiplication:

   (4x^3+2x^2-x+1) + (-3x^3 - 2x + 5)

3. Combine like terms: Identify terms with the same variable and power.

   • x^3 terms: 4x^3 - 3x^3 = x^3
   • x^2 terms: 2x^2 = 2x^2
   • x terms: -x - 2x = -3x
   • Constant terms: 1 + 5 = 6

4. Write the simplified expression:

   x^3 + 2x^2 - 3x + 6

Conclusion

By following these steps, we have successfully simplified the polynomial expression (4x^3+2x^2-x+1)-(3x^3+2x-5) to x^3 + 2x^2 - 3x + 6.

Remember, simplifying polynomial expressions is crucial for solving equations, finding solutions, and gaining a better understanding of the relationship between variables and constants.