Question

Use the Distributive Property to rewrite the expression $(2x-2)(x-6)$
(1 point)
$3x^{2}-10x-8$
$2x^{2}-14x+12$
D $x^{2}-8x+12$
D $2x^{2}+10x-10$

Answer 1

To use the Distributive Property (also known as the FOIL method for binomials) to rewrite the expression \((2x-2)(x-6)\), we will multiply each term in the first binomial by each term in the second binomial.

1. **First Term**:
\[
2x \cdot x = 2x^2
\]

2. **Outer Term**:
\[
2x \cdot (-6) = -12x
\]

3. **Inner Term**:
\[
-2 \cdot x = -2x
\]

4. **Last Term**:
\[
-2 \cdot (-6) = 12
\]

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

Next, we combine like terms:
\[
2x^2 - 14x + 12
\]

Thus, the expression \((2x-2)(x-6)\) simplifies to:
\[
\boxed{2x^{2}-14x+12}
\]