To apply the Distributive Property to the expression \((3x−1)(x−4)\), we need to distribute each term in the first parenthesis by each term in the second parenthesis.
The expression \((3x - 1)(x - 4)\) can be expanded as follows:
- \(3x \cdot x = 3x^2\)
- \(3x \cdot (-4) = -12x\)
- \(-1 \cdot x = -x\)
- \(-1 \cdot (-4) = 4\)
Now we combine these results:
\[ 3x^2 - 12x - x + 4 \]
Combine the \(x\) terms:
\[ 3x^2 - 13x + 4 \]
None of the options provided in your question exactly match this result, but from the responses given, the closest possibly correct manipulation might have been intended but was noted incorrectly in the list provided.
To summarize, the correct rewriting of the expression \((3x−1)(x−4)\) using the Distributive Property results in:
\[ 3x^2 - 13x + 4 \]
From the responses, you may want to double-check against the intended representations, as it seems none are exact. If you seek the one that closely resembles functional distribution, the steps followed were correct but the numerical combinations may need adjustments in your answer options.