Question

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

Answer 1

To use the Distributive Property (also known as the FOIL method for binomials) to rewrite the expression \((2x - 2)(x - 6)\), you can follow these steps:

1. **First**: Multiply the first terms in each binomial:
\(2x \cdot x = 2x^2\)

2. **Outer**: Multiply the outer terms:
\(2x \cdot (-6) = -12x\)

3. **Inner**: Multiply the inner terms:
\(-2 \cdot x = -2x\)

4. **Last**: Multiply the last terms in each binomial:
\(-2 \cdot (-6) = 12\)

Now, combine all these results:

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

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

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

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

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