according to the distributive property which is a way to rewrite the algebraic expression (3x - 1) (x - 4)

To rewrite the algebraic expression \((3x - 1)(x - 4)\) using the distributive property, you will distribute each term in the first parentheses across each term in the second parentheses.

Here’s how it works step-by-step:

1. Distribute \(3x\) to both \(x\) and \(-4\):
- \(3x \cdot x = 3x^2\)
- \(3x \cdot (-4) = -12x\)

2. Distribute \(-1\) to both \(x\) and \(-4\):
- \(-1 \cdot x = -x\)
- \(-1 \cdot (-4) = 4\)

Now, combine all the results:

\[
3x^2 - 12x - x + 4
\]

Next, combine the like terms (\(-12x\) and \(-x\)):

\[
3x^2 - 13x + 4
\]

So, the rewritten expression is:

\[
3x^2 - 13x + 4
\]