Let's expand and simplify the expression $3(w + 1) + 4(2w + 3)$.

Step-by-step solution:

1. Distribute the constants inside the parentheses: $3(w + 1) = 3w + 3$ $4(2w + 3) = 8w + 12$

2. Add the expanded terms: $3w + 3 + 8w + 12$

3. Combine like terms (terms with $w$ and constants): $(3w + 8w) + (3 + 12) = 11w + 15$

So, the fully simplified expression is: $11w + 15$

Would you like further details on any of the steps or have any questions?

Here are 5 related questions you might find useful:

1. How would the solution change if the coefficients in the parentheses were different?
2. Can you apply the distributive property to an expression with three terms inside parentheses?
3. What happens if one of the parentheses contains a negative number?
4. How do you handle expressions where variables appear in both parentheses, such as $3(x + y) + 4(y + z)$?
5. How would you simplify an expression that includes multiple sets of parentheses, like $2(3x + 1) + 5(2x + 4)$?

Tip: Always start by distributing constants or variables inside parentheses before combining like terms to simplify expressions effectively.