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

Question

(
2
𝑥
−
2
)
(
𝑥
−
6
)
.(1 point)
Responses

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

x2−8x+12
𝑥
2
−
8
𝑥
+
12
x squared minus 8 x plus 12

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

3x2−10x−8

Answer 1

To rewrite the expression \((2x−2)(x−6)\) using the Distributive Property, we can multiply each term in the first parentheses by each term in the second parentheses.

Let's distribute:

1. Multiply \(2x\) by \(x\): \[ 2x \cdot x = 2x^2 \]

2. Multiply \(2x\) by \(-6\): \[ 2x \cdot (-6) = -12x \]

3. Multiply \(-2\) by \(x\): \[ -2 \cdot x = -2x \]

4. Multiply \(-2\) by \(-6\): \[ -2 \cdot (-6) = 12 \]

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

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

So, the rewritten expression is: \[ 2x^2 - 14x + 12 \]

The correct response is: 2x²−14x+12 (which can also be stated as "2 x squared minus 14 x plus 12").