Question

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

A. 3x(x)+3x(−4)+−1(x)+−1(−4)

B. 3x^2−5x+4

C. 3x(−1)+3x(3x)+x(−4)+x(x)

D. 3x^2+6x+4

Answer 1

Well it HAS to be one so PICK THE CORRECT ONE CONNECTONS ACADEMY WOULDNT MESS AROUND LIKE THAT

Answer 2

To rewrite the algebraic expression (3x−1)(x−4) using the Distributive Property, we need to perform the multiplication by distributing each term in the first parentheses to each term in the second parentheses.

Here's how to do it:

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:

\[
3x^2 - 12x - x + 4 = 3x^2 - 13x + 4
\]

Now let's evaluate the options:

A. \(3x(x) + 3x(-4) - 1(x) - 1(-4)\) - This option is incorrect as it does not simplify the expression properly.

B. \(3x^2 - 5x + 4\) - This option is incorrect; the middle term is not -5x.

C. \(3x(-1) + 3x(3x) + x(-4) + x(x)\) - This option is incorrect as it does not correctly reflect the original expression.

D. \(3x^2 + 6x + 4\) - This option is incorrect; the terms do not match the expected output.

None of the provided options correctly represent the result of applying the Distributive Property to \((3x-1)(x-4)\).

The correct simplified expression is:

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

None of the choices provided in the options match.

Answer 3

I apologize for the confusion. Let’s review the options again, and ensure we provide an answer based on the closest correct interpretation, while also considering calculations for correctness.

We already simplified the expression \((3x - 1)(x - 4)\) to:

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

Now, let’s analyze each option with the goal of identifying the one that approaches the proper distribution.

**A.** \(3x(x) + 3x(-4) + -1(x) + -1(-4)\) - This option distributes correctly but simplifies incorrectly.

**B.** \(3x^2 - 5x + 4\) - Incorrect because the middle term does not match.

**C.** \(3x(-1) + 3x(3x) + x(-4) + x(x)\) - Incorrect as it does not follow the distribution properly.

**D.** \(3x^2 + 6x + 4\) - This is also incorrect.

The closest logical option based on your request would be **A**, as it at least attempts the correct distribution process, although it simplifies incorrectly later on.

So the best choice, despite the simplification issue, would be:

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

Thank you for your patience!