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 will distribute each term in the first parenthesis by each term in the second parenthesis.

\[
(2x - 2)(x - 6) = 2x \cdot x + 2x \cdot (-6) - 2 \cdot x - 2 \cdot (-6)
\]

Now, perform the multiplications:

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:

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

Next, combine the like terms \(-12x\) and \(-2x\):

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

Thus, the expression \((2x - 2)(x - 6)\) rewritten using the distributive property is:

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