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

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

x2−8x+12
x squared minus 8 x plus 12

Answer 1

To use the Distributive Property to rewrite the expression \((2x - 2)(x - 6)\), we'll apply the distributive property (also known as the FOIL method for binomials).

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, combine all these results:

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

Combine the like terms \(-12x - 2x\):

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

So, the rewritten expression is:

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

This corresponds to the third response option: \(2x^2 - 14x + 12\).