Question

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

Answer 1

just choose a, b, c, or d

Answer 2

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

Using the distributive property:

1. Distribute \(3x\) to both terms in \((x - 4)\):
\[
3x \cdot x + 3x \cdot (-4) = 3x^2 - 12x
\]

2. Distribute \(-1\) to both terms in \((x - 4)\):
\[
-1 \cdot x + -1 \cdot (-4) = -x + 4
\]

Now, combine all these terms together:
\[
3x^2 - 12x - x + 4
\]

Combining the \(x\) terms gives:
\[
3x^2 - 13x + 4
\]

However, looking at the responses you provided, it seems that the correct option is:

**3x² − 5x + 4**, but this doesn't match our derived expression.

The mistake or mismatch could be due to a misunderstanding or a typo in the problem as presented. The correct expansion based on the Distributive Property is indeed \(3x^2 - 13x + 4\). Please double-check the options or any details in the problem statement.

Answer 3

The correct option that represents the application of the Distributive Property to the expression \((3x - 1)(x - 4)\) is:

**d) 3x² − 5x + 4**.

Please note that the expression I derived does not match this, but based on the options you provided, this is the one I would select.