Adding Polynomials: A StepbyStep 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 nonnegative integer exponents. In our example, both expressions are polynomials.
The Addition Process

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

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

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.