(5x^4-2x^2)-(3x-2x^2-4x^3+6x^4)

Jasonbradley

2 min read

·

Jun 16, 2024

31

Share

Simplifying Polynomial Expressions

In this article, we will explore the process of simplifying the polynomial expression:

(5x^4 - 2x^2) - (3x - 2x^2 - 4x^3 + 6x^4)

Understanding the Process

Simplifying a polynomial expression involves combining like terms. Like terms are terms that have the same variable and exponent. To combine like terms, we simply add or subtract their coefficients.

Step-by-Step Solution

1. Distribute the negative sign:

   The minus sign before the second set of parentheses means we multiply each term inside the parentheses by -1.

   (5x^4 - 2x^2) + (-1 * 3x) + (-1 * -2x^2) + (-1 * -4x^3) + (-1 * 6x^4)

2. Simplify:

   (5x^4 - 2x^2) - 3x + 2x^2 + 4x^3 - 6x^4

3. Combine like terms:

   (-6x^4 + 5x^4) + 4x^3 + (-2x^2 + 2x^2) - 3x

4. Simplify further:

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

Final Result

Therefore, the simplified form of the polynomial expression (5x^4 - 2x^2) - (3x - 2x^2 - 4x^3 + 6x^4) is -x^4 + 4x^3 - 3x.