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

x2−8x+12
x squared minus 8 x plus 12

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

Answer 1

To use the Distributive Property to rewrite the expression \((2x−2)(x−6)\), we can apply the distributive property (also known as the FOIL method in the case of binomials) to multiply the terms:

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

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

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

Combining the like terms \(-12x\) and \(-2x\):
\[
2x^2 - 14x + 12
\]

So the expression \((2x−2)(x−6)\) simplifies to:
\[
2x^2 - 14x + 12
\]

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