Question

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

x2−8x+12
x squared minus 8 x plus 12

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

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

2x2−14x+12

Answer 1

To use the Distributive Property on the expression \( (2x - 2)(x - 6) \), we distribute each term in the first parenthesis across all terms in the second parenthesis.

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

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

Now combine all the terms:
\[
2x^2 - 12x - 2x + 12
\]

Combine like terms:
\[
2x^2 - (12x + 2x) + 12 = 2x^2 - 14x + 12
\]

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

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