Use the Distributive Property to rewrite the expression (2x−2)(x−6)

Question

.(1 point)
Responses

2x2+10x−10
2 x squared plus 10 x minus 10

3x2−10x−8
3 x squared minus 10 x minus 8

x2−8x+12
x squared minus 8 x plus 12

2x2−14x+12

Answer 1

To use the Distributive Property to rewrite the expression \((2x - 2)(x - 6)\), we will distribute each term in the first parenthesis by each term in the second parenthesis.

1. Distributing \(2x\): \[ 2x \cdot x = 2x^2 \] \[ 2x \cdot (-6) = -12x \]

2. Distributing \(-2\): \[ -2 \cdot x = -2x \] \[ -2 \cdot (-6) = 12 \]

Now, we combine all these results: \[ 2x^2 - 12x - 2x + 12 \]

Combine the like terms: \[ 2x^2 - 14x + 12 \]

So, the expression \((2x - 2)(x - 6)\) rewritten using the Distributive Property is: \[ 2x^2 - 14x + 12 \]

The correct response is: 2x² - 14x + 12.