Let's go through the expressions step by step and simplify them:

1. Simplifying $(7m + 3) + (3m + 1)$:

Combine like terms:

$(7m + 3) + (3m + 1) = 7m + 3m + 3 + 1 = 10m + 4$

2. Simplifying $(7m + 3) - (3m + 1)$:

Distribute the negative sign and combine like terms:

$(7m + 3) - (3m + 1) = 7m - 3m + 3 - 1 = 4m + 2$

3. Simplifying $2(7m + 3) + 3(3m + 1)$:

First, distribute the constants, then combine like terms:

$2(7m + 3) + 3(3m + 1) = (14m + 6) + (9m + 3) = 14m + 9m + 6 + 3 = 23m + 9$

4. Simplifying $2(7m + 3) - 3(3m + 1)$:

First, distribute the constants, then combine like terms:

$2(7m + 3) - 3(3m + 1) = (14m + 6) - (9m + 3) = 14m - 9m + 6 - 3 = 5m + 3$

Thus, the simplified expressions are:

1. $10m + 4$
2. $4m + 2$
3. $23m + 9$
4. $5m + 3$

Would you like any further details or explanations?

Related questions:

1. What is the process for distributing constants in algebraic expressions?
2. How do you recognize and combine like terms?
3. Can you explain how to deal with negative signs when simplifying expressions?
4. How do you handle expressions with multiple variables?
5. What are common mistakes to avoid when simplifying algebraic expressions?

Tip: When simplifying, always double-check the distribution of negative signs to avoid mistakes!