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

Question

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