Question

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

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
2 x squared minus 14 x plus 12

x2−8x+12

Answer 1

To use the Distributive Property to rewrite the expression \((2x - 2)(x - 6)\), we can use the FOIL method (First, Outer, Inner, Last) for binomials.

1. **First**: \(2x \cdot x = 2x^2\)
2. **Outer**: \(2x \cdot (-6) = -12x\)
3. **Inner**: \(-2 \cdot x = -2x\)
4. **Last**: \(-2 \cdot (-6) = 12\)

Now combine all these terms:

\[
2x^2 - 12x - 2x + 12 = 2x^2 - 14x + 12
\]

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

\[
\boxed{2x^2 - 14x + 12}
\]

This corresponds to the third response option.