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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 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 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

1 answer

To rewrite the expression (3x - 1)(x - 4) using the Distributive Property, we need to distribute each term in the first parentheses across each term in the second parentheses.

Let's perform the multiplication step-by-step:

  1. Distribute 3x:

    • 3x * x = 3x^2
    • 3x * (-4) = -12x

  2. Distribute -1:

    • -1 * x = -x
    • -1 * (-4) = 4

Now, combine all the results:

  • The \(3x^2\) stays as is.
  • Combine the terms involving x: \( -12x - x = -13x\).
  • The constant term is \( +4\).

Putting it all together, we get: \[ 3x^2 - 13x + 4 \]

Based on the options provided, none of them match the final result of \( 3x^2 - 13x + 4 \). Therefore, if you have to choose an answer based on the options given, there might be a mistake in the options. The correct expansion of the expression using the Distributive Property does result in \( 3x^2 - 13x + 4 \).