Question

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

3x2−5x+4
3 x squared minus 5 x plus 4

3x2+6x+4
3 x squared plus 6 x plus 4

3x(−1)+3x(3x)+x(−4)+x(x)
3 x left parenthesis negative 1 right parenthesis plus 3 x left parenthesis 3 x right parenthesis plus x left parenthesis negative 4 right parenthesis plus x left parenthesis x right parenthesis

3x(x)+3x(−4)+−1(x)+−1(−4)

Answer 1

To rewrite the algebraic expression (3x−1)(x−4) using the Distributive Property, we will multiply each term in the first expression by 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, combine all the terms together:
- \(3x^2 - 12x - x + 4\)

Combine like terms:
- \(-12x - x = -13x\)

Thus, the expression becomes:
- \(3x^2 - 13x + 4\)

Since this exact option isn't provided in your list, let's determine what is closest. The response options indicated seem to involve incorrect or misaligned sums.

If we analyze the options offered:

1. **3x² − 5x + 4**
- This does not match our result.

2. **3x² + 6x + 4**
- This does not match either.

3. **3x(−1) + 3x(3x) + x(−4) + x(x)**
- This expansion is incorrect as per the distributive property.

4. **3x(x) + 3x(−4) + −1(x) + −1(−4)**
- This expression computes correctly to what we started with, but it is not organized for simplification.

It seems that there might be errors in the response options offered. The precise simplified outcome of (3x−1)(x−4) using the distributive property equates to \(3x^2 - 13x + 4\). Please check if there was an error in the problem statement or any missing options.