ccording to the Distributive Property, which is a way to rewrite the algebraic expression (3x−1)(x−4)?(1 point) Responses 3x2+6x+4 3 x squared plus 6 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 3x2−5x+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

Answer 1

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

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: \[ 3x^2 - 12x - x + 4 \] Combine the like terms (i.e., \(-12x - x\)): \[ 3x^2 - 13x + 4 \]

Thus, the expression \((3x - 1)(x - 4)\) can be rewritten as: \[ 3x^2 - 13x + 4 \]

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