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

Question

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

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

Answer 1

To apply the Distributive Property to the expression (3x−1)(x−4), we can distribute each term in the first parenthesis by each term in the second parenthesis. The correct expansion is as follows:

1. Distribute 3x to both x and -4:

   • 3x * x = 3x²
   • 3x * -4 = -12x

2. Distribute -1 to both x and -4:

   • -1 * x = -x
   • -1 * -4 = 4

Now combine all the terms:

• 3x² - 12x - x + 4 = 3x² - 13x + 4

None of the options perfectly align with the final outcome, but the closest to the expression formed is:

• 3x² - 5x + 4, except note that from the detailed breakdown, the combination of -12x and -x gives -13x, which is not present in any option.

If the question specifically asks to rewrite the algebraic expression following the distributive property, the response that best reflects an expansion using the property is: 3x(x) + 3x(-4) + -1(x) + -1(-4)

However, if selecting based on mistaken simple addition (which miscalculated), one might be guided to 3x² - 5x + 4 by error, but emphasize it isn't accurate per thorough evaluation.

In summary, the best response based on the provided choices that reflects the method of using the distributive property is: 3x(x) + 3x(-4) + -1(x) + -1(-4)