According to the distributive property , which is a way to rewrite the algebraic expression?(3x-1)(x-4)

Question

A. 3x^2-5x+4
B. 3x(-1)+3x(3x)=x(-4)=x(x)
C. 3x^2+6x+4
D. 3x(x)+3x(-4)+-1(x)+-1(-4)

Answer 1

To rewrite the expression \((3x - 1)(x - 4)\) using the distributive property, we can follow these steps:

1. Distribute \(3x\) to both terms in the second parenthesis: \[ 3x \cdot x + 3x \cdot (-4) = 3x^2 - 12x \]

2. Next, distribute \(-1\) to both terms in the second parenthesis: \[ -1 \cdot x + (-1) \cdot (-4) = -x + 4 \]

3. Now, combine all these results: \[ 3x^2 - 12x - x + 4 = 3x^2 - 13x + 4 \]

None of the provided answer choices result in the perfectly simplified version of the expression, but it appears that option D (which describes the distribution process) is the most closely related to the distributive property approach.

Thus, the answer is: D. \(3x(x) + 3x(-4) + -1(x) + -1(-4)\)