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

To rewrite the expression \( (3x - 1)(x - 4) \) using the Distributive Property, we apply the distributive method (also known as FOIL for binomials).

1. **First**: Multiply the first terms:
\[
3x \cdot x = 3x^2
\]

2. **Outer**: Multiply the outer terms:
\[
3x \cdot (-4) = -12x
\]

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

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

Now, combine all of these results:
\[
3x^2 - 12x - x + 4
\]
Combine like terms:
\[
3x^2 - 13x + 4
\]

Thus, the final expression is:
\[
3x^2 - 13x + 4
\]

Given the options provided, let's check them:
- A) \( 3x(-1) + 3x(3x) + x(-4) + x(x) \) - Incorrect format
- B) \( 3x(x) + 3x(-4) + -1(x) + -1(-4) \) - This is correct but doesn't match the final reduction.
- C) \( 3x^2 + 6x + 4 \) - Incorrect
- D) \( 3x^2 - 5x + 4 \) - Incorrect

None of these options directly match \( 3x^2 - 13x + 4 \), which appears to be the intended result.

Upon reviewing, it seems that option B is the closest in terms of steps, but it ultimately doesn’t give the fully reduced polynomial.

So, while Option B expresses the expansion correctly before combining terms, none of the options provided yield the complete and correct simplified result. The correct rewritten expression is:
\[ 3x^2 - 13x + 4 \] (not in the options).