Question

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

3x2−10x−8
3
x
2
−
10
x
−
8
3 x squared minus 10 x minus 8

x2−8x+12
x
2
−
8
x
+
12
x squared minus 8 x plus 12

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

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

Answer 1

To use the Distributive Property to expand the expression \((2x - 2)(x - 6)\), we can apply the distributive property (also known as the FOIL method for binomials) as follows:

1. **Multiply the first terms**:
\[
2x \cdot x = 2x^2
\]

2. **Multiply the outer terms**:
\[
2x \cdot (-6) = -12x
\]

3. **Multiply the inner terms**:
\[
-2 \cdot x = -2x
\]

4. **Multiply the last terms**:
\[
-2 \cdot (-6) = 12
\]

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

Next, combine the like terms:
\[
2x^2 - 14x + 12
\]

Thus, the expression \((2x - 2)(x - 6)\) expands to:
\[
\boxed{2x^2 - 14x + 12}
\]

This matches the third response option.