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 will apply the property by distributing each term in the first expression to each term in the second expression.

1. Distributing \(3x\):

   • \(3x \cdot x = 3x^2\)
   • \(3x \cdot (-4) = -12x\)

2. Distributing \(-1\):

   • \(-1 \cdot x = -x\)
   • \(-1 \cdot (-4) = 4\)

Now, we combine all these results together: \[ 3x^2 - 12x - x + 4 \] Combine the like terms \(-12x\) and \(-x\): \[ 3x^2 - 13x + 4 \]

Thus, the rewritten expression using the Distributive Property is \(3x^2 - 13x + 4\).

Now, let's review the choices:

• A: \(3x(-1) + 3x(3x) + x(-4) + x(x)\): Incorrect; does not correctly apply the Distributive Property.
• B: \(3x^2 - 5x + 4\): Incorrect.
• C: \(3x^2 + 6x + 4\): Incorrect.
• D: \(3x(x) + 3x(-4) + -1(x) + -1(-4)\): Correctly shows the use of Distributive Property, though it doesn't combine the terms.

Since we are looking for a correct answer based on applying the Distributive Property, the best option given is:

D. \(3x(x) + 3x(-4) + -1(x) + -1(-4)\)

This correctly expresses the application of the Distributive Property, even if it doesn't simplify to the final factored form.