Question

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

Answer 1

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

Here’s how it’s done step-by-step:

1. Distribute \( 2x \) to both \( x \) and \( -6 \):
\[
2x \cdot x + 2x \cdot (-6) = 2x^2 - 12x
\]

2. Distribute \( -2 \) to both \( x \) and \( -6 \):
\[
-2 \cdot x + (-2) \cdot (-6) = -2x + 12
\]

3. Now, combine all the terms from steps 1 and 2:
\[
2x^2 - 12x - 2x + 12
\]

4. Combine the like terms \(-12x\) and \(-2x\):
\[
2x^2 - 14x + 12
\]

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