Question

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

3x2−10x−8
3
x
2
−
10
x
−
8
3 x squared minus 10 x minus 8

2x2+10x−10
2
x
2
+
10
x
−
10
2 x squared plus 10 x minus 10

2x2−14x+12
2
x
2
−
14
x
+
12
2 x squared minus 14 x plus 12

x2−8x+12

Answer 1

To use the Distributive Property to rewrite the expression \((2x - 2)(x - 6)\), we can apply the formula \(a(b + c) = ab + ac\) and distribute each term in the first parenthesis by each term in the second parenthesis.

Here are the steps:

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

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

3. Now combine all these results:
\[
2x^2 - 12x - 2x + 12
\]

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

So, the expression \((2x - 2)(x - 6)\) rewritten using the Distributive Property is:
\[
\boxed{2x^2 - 14x + 12}
\]

This corresponds to the third option in your provided responses.