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We are tasked with finding the factored form of the expression:

\[
2x(4x + 3) - (4x + 3)
\]

### Step-by-Step Solution:

1. **Factor out the common term:**
   Notice that both terms in the expression have a common factor of \((4x + 3)\). We can factor this out as follows:

   \[
   (4x + 3)\left(2x - 1\right)
   \]

   The expression simplifies directly to:

   \[
   (4x + 3)(2x - 1)
   \]

### Answer:

The factored form is \((4x + 3)(2x - 1)\), which corresponds to **Option D**.

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Would you like further details or have any questions?

Here are five related questions:
1. How do you determine the greatest common factor when factoring?
2. What is the difference between factoring and expanding expressions?
3. How do you factor quadratic expressions that don’t have common terms?
4. Can all binomials be factored easily like this one?
5. What is the role of grouping in factoring polynomials?

**Tip:** Always check for a common factor when simplifying expressions—it can often make factoring much easier.

Which is the factored form of 2x(4x + 3) - (4x + 3)?

Learn how to factor the expression 2x(4x + 3) - (4x + 3) using the distributive property and common factoring. This algebra problem is ideal for students in Grades 7-10 looking to strengthen their factoring skills.

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