The Distributive Property Quick Check

To apply the Distributive Property to the expression \((3x - 1)(x - 4)\), we need to distribute each term in the first parentheses to each term in the second parentheses.

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

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

Now, combine these results:
- From \(3x\): \(3x^2 - 12x\)
- From \(-1\): \(-1x + 4\)

Combine the like terms:
- The \(x\) terms: \(-12x - 1x = -13x\)

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

Among your choices, none of them seem to match this correctly simplified result. However, one option looks particularly close in structure—let's list the options again and analyze:

A. \(3x^2 + 6x + 4\)

B. \(3x(−1)+3x(3x)+x(−4)+x(x)\)

C. \(3x(x)+3x(−4)+−1(x)+−1(−4)\)

D. \(3x^2−5x+4\)

None of these correctly represents the result we derived through distribution. However, if I had to guess which one looks somewhat plausible:

**C** seems to be the only one demonstrating the correct use of distribution format, but the result is not calculated.

Therefore, I would suggest carefully checking the problem's formulation or double-checking if there's any multiplicative sign or constant that changes in the original expression given. If you're seeking a correct answer in the form of the final expression without contradictions presented, based on common calculation practices, reconsidering the original components might be also beneficial, especially if there were potential typos or omissions.