Question

Question

Use the Distributive Property to combine like terms and simplify the expression.

2 left parenthesis 2z plus 4 right parenthesis minus 2 left parenthesis 3z plus 10 right parenthesis
(1 point)
Responses

Negative 14z
Image with alt text: Negative 14z

Negative 2z minus 12
Image with alt text: Negative 2z minus 12

Negative 2z plus 28
Image with alt text: Negative 2z plus 28

Negative 2z plus 14
Image with alt text: Negative 2z plus 14

Answer 1

To simplify the expression \( 2(2z + 4) - 2(3z + 10) \) using the Distributive Property, follow these steps:

1. Distribute \( 2 \) in \( 2(2z + 4) \): \[ 2 \cdot 2z + 2 \cdot 4 = 4z + 8 \]

2. Distribute \( -2 \) in \( -2(3z + 10) \): \[ -2 \cdot 3z - 2 \cdot 10 = -6z - 20 \]

3. Combine the results: \[ 4z + 8 - 6z - 20 \]

4. Combine like terms:

   • For the \( z \) terms: \( 4z - 6z = -2z \)
   • For the constant terms: \( 8 - 20 = -12 \)

5. The simplified expression is: \[ -2z - 12 \]

Therefore, the final answer is Negative 2z minus 12.