Use the Distributive Property to rewrite the expression (2x−2)(x−6) .(1 point)

Question

Responses

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

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

2x2−14x+12
2 x squared minus 14 x plus 12

x2−8x+12
x squared minus 8 x plus 12

Answer 1

To apply the Distributive Property to the expression \((2x - 2)(x - 6)\), you need to distribute each term in the first expression by each term in the second expression.

Here's how it's done step-by-step:

1. Distribute \(2x\) to both \(x\) and \(-6\): \[ 2x \cdot x = 2x^2 \] \[ 2x \cdot (-6) = -12x \]

2. Distribute \(-2\) to both \(x\) and \(-6\): \[ -2 \cdot x = -2x \] \[ -2 \cdot (-6) = 12 \]

3. Now, combine all the like terms: \[ 2x^2 - 12x - 2x + 12 = 2x^2 - 14x + 12 \]

So, the expression \((2x - 2)(x - 6)\) rewritten using the Distributive Property is

\(2x^2 - 14x + 12\).

Thus, the correct response is: 2x² − 14x + 12.