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

Question

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

GPT-4o mini · Answer

To rewrite the algebraic expression $(3x - 1)(x - 4)$ using the Distributive Property, you need to multiply each term in the first expression by each term in the second expression. Let's do the multiplication: 1. Multiply $3x$ by both terms in $(x - 4)$: - $3x \cdot x = 3x^2$ - $3x \cdot (-4) = -12x$ 2. Now, multiply $-1$ by both terms in $(x - 4)$: - $-1 \cdot x = -x$ - $-1 \cdot (-4) = 4$ Now, combine these results: $$ 3x^2 - 12x - x + 4 $$ Combine the $ -12x $ and $-x$: $$ 3x^2 - 13x + 4 $$ So, the expression $(3x - 1)(x - 4)$ simplifies to: $$ 3x^2 - 13x + 4 $$ However, if we compare those options, none of them gives exactly what we calculated. The closest match is $3x^2 - 5x + 4$, but it is incorrect based on the initial calculation. The correct expansion should read: $$ 3x^2 - 13x + 4 $$ **Note:** It seems that none of the provided choices are correct based on the expression provided.