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

Question

Responses

3x2+6x+4
3 x squared plus 6 x plus 4

3x(−1)+3x(3x)+x(−4)+x(x)
3 x left parenthesis negative 1 right parenthesis plus 3 x left parenthesis 3 x right parenthesis plus x left parenthesis negative 4 right parenthesis plus x left parenthesis x right parenthesis

3x2−5x+4
3 x squared minus 5 x plus 4

3x(x)+3x(−4)+−1(x)+−1(−4)

Answer 1

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

Here's the step-by-step breakdown:

1. Distribute \(3x\):

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

2. Distribute \(-1\):

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

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

Combine the like terms \(-12x\) and \(-x\): \[ 3x^2 - 13x + 4 \]

However, it seems that \(-12x\) was not one of the provided responses. The closest and correct option appears to be:

• 3x^2 - 5x + 4

Please double-check the calculations or re-evaluate the given choices as none exactly match the expanded expression \(3x^2 - 13x + 4\). The correctly rewritten expression according to the Distributive Property of \((3x - 1)(x - 4)\) is \(3x^2 - 13x + 4\).