Question

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

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

x2−8x+12
x squared minus 8 x plus 12

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

3x2−10x−8

Answer 1

To use the Distributive Property to rewrite the expression \((2x−2)(x−6)\), we'll distribute each term in the first parentheses to each term in the second parentheses.

1. Distribute \(2x\):
- \(2x \cdot x = 2x^2\)
- \(2x \cdot (-6) = -12x\)

2. Distribute \(-2\):
- \(-2 \cdot x = -2x\)
- \(-2 \cdot (-6) = 12\)

Now, we combine all these terms:

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

Combine the like terms \(-12x\) and \(-2x\):

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

So, the expression \((2x−2)(x−6)\) simplifies to:

**2x² - 14x + 12**

Thus, the correct response is:

**2 x squared minus 14 x plus 12**.