Question

Use the distributive property to rewrite the expression: (2x-2)(x-6)

Answer 1

To apply the distributive property to rewrite the expression \((2x-2)(x-6)\), we can distribute each term in the first parentheses across each term in the second parentheses.

Here’s how you do it step by step:

1. Distribute \(2x\) to both terms in \((x - 6)\):
- \(2x \cdot x = 2x^2\)
- \(2x \cdot -6 = -12x\)

2. Distribute \(-2\) to both terms in \((x - 6)\):
- \(-2 \cdot x = -2x\)
- \(-2 \cdot -6 = 12\)

Now, combine all the results:
\[
2x^2 - 12x - 2x + 12
\]

Next, combine the like terms \(-12x\) and \(-2x\):
\[
2x^2 - 14x + 12
\]

So, the expression \((2x-2)(x-6)\) rewritten using the distributive property is:
\[
2x^2 - 14x + 12
\]