Question

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

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

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

Answer 1

To rewrite the algebraic expression \((3x - 1)(x - 4)\) using the Distributive Property, you can distribute each term in the first parenthesis by each term in the second parenthesis:

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 the results:
- \(3x^2 - 12x - x + 4\)

Combine the like terms \(-12x\) and \(-x\):
- \(-12x - x = -13x\)

Thus, the expression simplifies to:
- \(3x^2 - 13x + 4\)

The correct rewritten form from your provided options is not present. However, if it were corrected, it would be option similar to \(3x^2 - 13x + 4\).

If I must select the best fitting response from the options provided, without any correct total matches, the closest option mathematically in terms of distributing properly would be the second option:

**3x(x) + 3x(-4) + -1(x) + -1(-4)** which represents the correct distribution, but the results derived from those do not match the final outcome of \(3x^2 - 13x + 4\).

None of the provided options correctly reflect the outcome of the distribution according to the Distributive Property.