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The problem displayed is asking for the product of two polynomials:

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

To solve this, we use the distributive property (also known as the FOIL method for binomials):

1. **First**: Multiply the first terms from each binomial:
   \[
   2x \cdot x = 2x^2
   \]

2. **Outer**: Multiply the outer terms:
   \[
   2x \cdot (-4) = -8x
   \]

3. **Inner**: Multiply the inner terms:
   \[
   1 \cdot x = x
   \]

4. **Last**: Multiply the last terms:
   \[
   1 \cdot (-4) = -4
   \]

Now, sum all these products together:
\[
2x^2 - 8x + x - 4 = 2x^2 - 7x - 4
\]

So the product of the polynomials is:

\[
2x^2 - 7x - 4
\]

Would you like further clarification or details?

Here are five related questions to expand on this:
1. What is the distributive property and how is it applied to binomials?
2. How does the FOIL method work for multiplying binomials?
3. Can you apply the distributive property to three polynomials?
4. How would you factor the expression \( 2x^2 - 7x - 4 \)?
5. What are some common mistakes to avoid when using the distributive property?

**Tip**: When multiplying binomials, double-check the signs for each term to avoid errors.

Find the product of the polynomials (2x + 1)(x - 4).

Learn how to multiply polynomials using the distributive property in this example: (2x + 1)(x - 4). This step-by-step solution highlights key algebraic concepts, suitable for students in Grades 7-9.

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