Let's expand the given expression step by step.

The expression is:

$4(2b + 3d) - (3b + 4d)$

Step 1: Distribute the constants.

• Distribute $4$ to both terms inside the first parenthesis $(2b + 3d)$:

$4(2b) + 4(3d) = 8b + 12d$

• Now distribute $-1$ to both terms inside the second parenthesis $(3b + 4d)$:

$-1(3b) - 1(4d) = -3b - 4d$

Step 2: Combine like terms.

Now, we combine the terms:

$8b + 12d - 3b - 4d$

• Combine the $b$-terms: $8b - 3b = 5b$
• Combine the $d$-terms: $12d - 4d = 8d$

Final expanded expression:

$5b + 8d$

Would you like further explanation on any step, or do you have any questions?

Here are five related questions:

1. How do you distribute when there's a negative sign outside the parentheses?
2. Can you apply the distributive property with more complex terms?
3. What happens if there are variables with exponents in the terms you are distributing?
4. How would this process change if you were factoring instead of expanding?
5. What are the common mistakes to avoid when distributing negative signs?

Tip: Always be careful with signs when expanding, especially when there are negative terms!