According to the Distributive Property, which is a way to rewrite the algebraic expression (3x-1)(x-4)

To rewrite the algebraic expression \((3x-1)(x-4)\) using the Distributive Property, we can distribute each term in the first parentheses by each term in the second parentheses.

Let's do this step-by-step:

1. Distribute \(3x\) to both terms in \((x - 4)\):
- \(3x \cdot x = 3x^2\)
- \(3x \cdot (-4) = -12x\)

2. Distribute \(-1\) to both terms in \((x - 4)\):
- \(-1 \cdot x = -x\)
- \(-1 \cdot (-4) = 4\)

Now combine all the terms:
\[
3x^2 - 12x - x + 4
\]
Combining like terms:
\[
3x^2 - 13x + 4
\]

None of the provided answer options match exactly, but evaluating the options given:

- **A.** \(3x(-1)+3x(3x)+x(-4)+x(x)\) → This does not represent the expression correctly.
- **B.** \(3x^2 - 5x + 4\) → Incorrect because the middle term doesn't match.
- **C.** \(3x(x) + 3x(-4) + -1(x) + -1(-4)\) → This represents the correct process of distributing.
- **D.** \(3x^2 + 6x + 4\) → Incorrect because the terms do not match.

Based on this analysis, the best answer would be **C**, as it reflects the correct distribution process. However, it does not directly reduce to the final expression, which is \(3x^2 - 13x + 4\).