Question

According to the Distributive Property, which is a way to rewrite the algebraic expression (3x - 1)(x - 4) (1 point)
3x^2 + 6x + 4
3x(- 1) + 3x(3x) + x(- 4) + x(x)
3x^2 - 5x + 4
3x(x) + 3x(- 4) + -1(x) + -1(- 4)

Answer 1

To rewrite the algebraic expression \((3x - 1)(x - 4)\) using the Distributive Property, you need to multiply each term in the first expression by each term in the second expression.

Let's do the multiplication:

1. Multiply \(3x\) by both terms in \((x - 4)\):
- \(3x \cdot x = 3x^2\)
- \(3x \cdot (-4) = -12x\)

2. Now, multiply \(-1\) by both terms in \((x - 4)\):
- \(-1 \cdot x = -x\)
- \(-1 \cdot (-4) = 4\)

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

Combine the \( -12x \) and \(-x\):
\[
3x^2 - 13x + 4
\]

So, the expression \((3x - 1)(x - 4)\) simplifies to:
\[
3x^2 - 13x + 4
\]

However, if we compare those options, none of them gives exactly what we calculated. The closest match is \(3x^2 - 5x + 4\), but it is incorrect based on the initial calculation.

The correct expansion should read:
\[
3x^2 - 13x + 4
\]

**Note:** It seems that none of the provided choices are correct based on the expression provided.