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

Question

3z ^ 2 + 6z + 4
3x(- 1) + 3x(3x) + x(- 4) + x(x)
3x ^ 2 - 5x + 4
3x(x) + 3x(- 4) - (x) - (- 4)

Answer 1

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

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: \[ 3x^2 - 12x - x + 4 \]

Combine the terms involving \(x\): \[ 3x^2 - 13x + 4 \]

Thus, the correct rewritten expression is: \[ 3x^2 - 13x + 4 \]

Looking at the options provided, the closest response that aligns with this is not explicitly given. However, it seems that none of the options you listed match the result of the Distributive Property applied to the expression \((3x - 1)(x - 4)\).