Question

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

A. 3x(-1)+3x(3x)+x(-4)+x(x)
B. 3x^2-5x+4
C. 3x^2+6x+4
D. 3x(x)+3x(-4)+-1(x)+-1(-4)

Answer 1

To rewrite the expression \((3x-1)(x-4)\) using the Distributive Property, we will apply the property by distributing each term in the first expression to each term in the second expression.

1. Distributing \(3x\):
- \(3x \cdot x = 3x^2\)
- \(3x \cdot (-4) = -12x\)

2. Distributing \(-1\):
- \(-1 \cdot x = -x\)
- \(-1 \cdot (-4) = 4\)

Now, we combine all these results together:
\[
3x^2 - 12x - x + 4
\]
Combine the like terms \(-12x\) and \(-x\):
\[
3x^2 - 13x + 4
\]

Thus, the rewritten expression using the Distributive Property is \(3x^2 - 13x + 4\).

Now, let's review the choices:
- A: \(3x(-1) + 3x(3x) + x(-4) + x(x)\): Incorrect; does not correctly apply the Distributive Property.
- B: \(3x^2 - 5x + 4\): Incorrect.
- C: \(3x^2 + 6x + 4\): Incorrect.
- D: \(3x(x) + 3x(-4) + -1(x) + -1(-4)\): Correctly shows the use of Distributive Property, though it doesn't combine the terms.

Since we are looking for a correct answer based on applying the Distributive Property, the best option given is:

**D. \(3x(x) + 3x(-4) + -1(x) + -1(-4)\)**

This correctly expresses the application of the Distributive Property, even if it doesn't simplify to the final factored form.