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

Question

?(1 point)
Responses

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)
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 need to distribute 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 like terms \(-12x - x\):

• \(3x^2 - 13x + 4\)

None of the provided responses match this result. However, the closest option in spirit of the process (not directly), corresponds with distributing but contains errors in calculations.

The correct expression using the Distributive Property is:

• \(3x^2 - 13x + 4\)

None of the provided responses are correct based on this expansion, and the second option you present, \(3x^2−5x+4\), also does not capture it correctly.

If you need to check them again, or reference to choose any of the options above for educational purposes, feel free to let me know.