(13m^4+2)+(m^4n^2+2-2m^4)-(-13m^2n^3+5m^4)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions

This article will guide you through the process of simplifying the following polynomial expression:

(13m^4 + 2) + (m^4n^2 + 2 - 2m^4) - (-13m^2n^3 + 5m^4)

Understanding the Steps

Simplifying polynomial expressions involves combining like terms. Like terms are terms that have the same variables raised to the same powers. Here's a breakdown of the steps:

1. Distribute the negative sign: The minus sign in front of the last set of parentheses means we multiply each term inside by -1.

2. Identify like terms: Look for terms with the same variables and exponents.

3. Combine like terms: Add or subtract the coefficients of like terms.

Simplifying the Expression

Let's apply these steps to our expression:

1. Distribute the negative sign: (13m^4 + 2) + (m^4n^2 + 2 - 2m^4) + 13m^2n^3 - 5m^4

2. Identify like terms:

   • m^4 terms: 13m^4 - 2m^4 - 5m^4
   • m^4n^2 term: m^4n^2
   • m^2n^3 term: 13m^2n^3
   • Constant terms: 2 + 2

3. Combine like terms:

   • m^4 terms: (13 - 2 - 5)m^4 = 6m^4
   • m^4n^2 term: m^4n^2
   • m^2n^3 term: 13m^2n^3
   • Constant terms: 2 + 2 = 4

Simplified Expression

Therefore, the simplified expression is:

6m^4 + m^4n^2 + 13m^2n^3 + 4