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

Jasonbradley

2 min read

·

Jun 16, 2024

24

Share

Simplifying Polynomial Expressions

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

Understanding the Expression

The expression involves two sets of parentheses containing polynomial terms. The "-" sign between the parentheses indicates that we need to subtract the second set of terms from the first.

Simplifying the Expression

1. Distribute the negative sign:

   • The negative sign in front of the second set of parentheses means we multiply each term inside the parentheses by -1.

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

2. Combine like terms:

   • Identify terms with the same variable and exponent and combine their coefficients.

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

3. Simplify further:

   2x^3 - 2x^2 + 4x + 2

Final Result

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