Question

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

3x(x) + 3x(-4) + -1(x) + -1(-4)
3x to the power of 2 + 6x + 4
3x(-1) + 3x(3x) + x(-4) + x(x)
3x to the power of 2 - 5x + 4

Answer 1

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

Let's break it down:

1. Multiply \(3x\) by \(x\):
\[
3x \cdot x = 3x^2
\]

2. Multiply \(3x\) by \(-4\):
\[
3x \cdot (-4) = -12x
\]

3. Multiply \(-1\) by \(x\):
\[
-1 \cdot x = -x
\]

4. Multiply \(-1\) by \(-4\):
\[
-1 \cdot (-4) = 4
\]

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

Combine like terms:
\[
3x^2 - 13x + 4
\]

Thus, the simplified expression for \((3x - 1)(x - 4)\) is:
\[
3x^2 - 13x + 4
\]

None of the options you provided are fully correct, but the closest expressions would be in terms of the signs and operations applied.