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

Question

make sure ur 100000000% sure you're correct

Answer 1

To use the Distributive Property to rewrite the expression \((3x - 1)(x - 4)\), we will apply distribution:

1. Distribute \(3x\) to both terms in the second expression: \[ 3x \cdot x + 3x \cdot (-4) = 3x^2 - 12x \]

2. Distribute \(-1\) to both terms in the second expression: \[ -1 \cdot x + (-1) \cdot (-4) = -x + 4 \]

Now, we combine the results: \[ 3x^2 - 12x - x + 4 = 3x^2 - 13x + 4 \]

Thus, the correct rewritten expression of \((3x - 1)(x - 4)\) is: \[ \boxed{3x^2 - 13x + 4} \]

None of the provided options in your question seem to match this correctly simplified expression.

Answer 2

One of them have to be the correct answer. It's the only options the school provided me

Answer 3

I apologize for the confusion. Let's go through the options you provided and determine which one correctly reflects the expansion of \((3x - 1)(x - 4)\).

Given expression:

\((3x - 1)(x - 4)\)

Applying the Distributive Property (Foil Method):

1. First terms: \(3x \cdot x = 3x^2\)
2. Outer terms: \(3x \cdot (-4) = -12x\)
3. Inner terms: \(-1 \cdot x = -x\)
4. Last terms: \(-1 \cdot (-4) = 4\)

Now, combine all these results: \[ 3x^2 - 12x - x + 4 = 3x^2 - 13x + 4 \]

Evaluating options:

1. Option 1: \(3x^2 - 5x + 4\) (Incorrect)
2. Option 2: \(3x(x) + 3x(-4) + -1(x) + -1(-4)\)
   • This option simplifies correctly to \(3x^2 - 12x - x + 4 = 3x^2 - 13x + 4\) (Correct representation in terms of distribution, but not simplified)
3. Option 3: \(3x(-1) + 3x(3x) + x(-4) + x(x)\) (Incorrect)
4. Option 4: \(3x^2 + 6x + 4\) (Incorrect)

Given the way you're presented this information, Option 2 is the correct expansion because it accurately represents the distribution steps, even though it hasn't been simplified into the final form.

So, the best answer according to the options you provided is: \(3x(x) + 3x(-4) + -1(x) + -1(-4)\)

Thank you for your understanding!