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

Question

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

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

x2−8x+12
x squared minus 8 x plus 12

2x2+10x−10

Answer 1

To use the Distributive Property to rewrite the expression \((2x−2)(x−6)\), we will distribute each term in the first parentheses by each term in the second parentheses.

The expression is:

\[ (2x - 2)(x - 6) \]

Now we distribute:

1. \(2x \cdot x = 2x^2\)
2. \(2x \cdot (-6) = -12x\)
3. \(-2 \cdot x = -2x\)
4. \(-2 \cdot (-6) = 12\)

Now combine all these results:

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

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

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

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

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

Thus, the correct expression from your options is:

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