To find the sum of the terms 5m, 3n, p, 5p, 3n, and 2n m, you need to combine like terms. Like terms are those that have the same variable parts.
1. **Identify the like terms**:
- Terms with ‘m’: 5m
- Terms with ‘n’: 3n, 3n, 2n m (note: 2n m can be broken down as 2n*m for clarity)
(Here we can also assess that 3n and 3n can be combined) - Terms with ‘p’: p, 5p
2. **Combine like terms**:
- For m: the only term is 5m, which remains as 5m.
- For n: combining the like terms gives you:
3n + 3n + (2n * m) = 6n + 2n*m. - For p: combining gives you:
p + 5p = 6p.
3. **Put it all together**:
The final sum is: 5m + 6n + 6p + 2n*m.
This expression represents the combined sum of the original terms and is your simplified answer.
In conclusion, when working with algebraic expressions, always look for like terms that you can combine to simplify your answer. This not only makes the expression easier to understand but also helps in further calculations.