Question

Use the Distributive Property to rewrite the expression (2x−2)(x−6) .
3x^2 - 10x - 8
x^2 - 8x + 12
2x^2 - 14x + 12
2x^2 + 10x - 10

Answer 1

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

1. Start with \((2x - 2)(x - 6)\).
2. Distribute \(2x\) to both terms in the second parentheses:
\[
2x \cdot x + 2x \cdot (-6) = 2x^2 - 12x
\]

3. Next, distribute \(-2\) to both terms in the second parentheses:
\[
-2 \cdot x + (-2) \cdot (-6) = -2x + 12
\]

4. Now combine all the terms together:
\[
2x^2 - 12x - 2x + 12 = 2x^2 - 14x + 12
\]

So, the expression \((2x - 2)(x - 6)\) simplifies to:

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

This matches the option **\(2x^2 - 14x + 12\)**.