simplify the expression: (2x+1)(x-4)

To simplify the expression \((2x + 1)(x - 4)\), we will use the distributive property (also known as the FOIL method for binomials).

1. First, multiply the first terms:
\(2x \cdot x = 2x^2\)

2. Next, multiply the outer terms:
\(2x \cdot (-4) = -8x\)

3. Then, multiply the inner terms:
\(1 \cdot x = x\)

4. Finally, multiply the last terms:
\(1 \cdot (-4) = -4\)

Now, combine all these results:
\[
2x^2 - 8x + x - 4
\]

Combine the like terms \(-8x\) and \(x\):
\[
2x^2 - 7x - 4
\]

Thus, the simplified expression is:
\[
2x^2 - 7x - 4
\]

The correct answer is **D: 2x^2 - 7x - 4**.