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

Jasonbradley

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Jun 16, 2024

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Adding Polynomials: A Step-by-Step Guide

This article will guide you through the process of adding two polynomials: (5m³ + 2m² - m) + (m² + 4m - 2).

Understanding Polynomials

Polynomials are expressions that consist of variables and constants, combined using addition, subtraction, multiplication, and non-negative integer exponents. In our example, both expressions are polynomials.

The Addition Process

1. Identify like terms: Look for terms that have the same variable and exponent. In this case, we have:

   • m³ terms: 5m³
   • m² terms: 2m² and m²
   • m terms: -m and 4m
   • Constant terms: -2

2. Combine like terms: Add the coefficients of each like term. Remember that if a term has no coefficient, it's understood to be 1.

   • m³ terms: 5m³
   • m² terms: 2m² + 1m² = 3m²
   • m terms: -1m + 4m = 3m
   • Constant terms: -2

3. Write the simplified polynomial: Combine the results of step 2 to get the final answer.

Therefore, (5m³ + 2m² - m) + (m² + 4m - 2) = 5m³ + 3m² + 3m - 2

Key Points to Remember

• Only like terms can be combined.
• When combining like terms, only the coefficients are added.
• The exponents of the variables remain unchanged.

By following these steps, you can confidently add any two polynomials.