To distribute $(x - 4)(2x + 3)$ using the distributive property, we expand it by distributing $(x - 4)$ to both terms inside $(2x + 3)$:

$(x - 4)(2x + 3) = (x - 4)(2x) + (x - 4)(3)$

Looking at the answer choices:

• Option A: $(x - 4)(2x) + (x - 4)(3)$ — This matches the correct distribution.
• Option B: $(x - 4)(2x) + (2x)(3)$ — This is incorrect because it misapplies the distributive property by treating $(2x)$ independently.
• Option C: $(x)(2x + 3) + (x - 4)$ — This is incorrect because it only distributes $x$, not $(x - 4)$.
• Option D: $(x)(2x) + 3(x) + 2x + 3$ — This is incorrect because it breaks down the terms in an incorrect manner.

The correct answer is:

A. $(x - 4)(2x) + (x - 4)(3)$

Would you like further details or have any questions?

Here are some related questions to expand on this topic:

1. How do you fully expand $(x - 4)(2x + 3)$ after distribution?
2. Why is the distributive property important in algebra?
3. How does distribution work when there are more than two terms?
4. What happens if we have negative numbers in distribution?
5. How can we apply the distributive property with variables raised to powers?

Tip: Remember, when applying the distributive property, each term in the first expression must multiply each term in the second expression.