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

Question

?(1 point)
Responses

3x2−5x+4
3 x squared minus 5 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

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

3x2+6x+4

Answer 1

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

1. Distributing \(3x\):

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

2. Distributing \(-1\):

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

Now, combine all of these results: \[ 3x^2 - 12x - 1x + 4 \] Combine the like terms: \[ 3x^2 - 13x + 4 \]

It looks like there is a small mistake in seeing the options. None of them verify this expression.

However, based on what you have given, the expression that best aligns with the associative distribution is:

3x(−1) + 3x(−4) + −1(x) + −1(−4)

Which equals: \(-3x - 12 + 1 - 4\)

Although none match \(3x^2 - 13x + 4\) directly, look for the expression arrangement.

In the simplest reformed equation, it should simplify to 3x^2 - 13x + 4 most accurately based on original distribution.