Find the product. Simplify your answer. $$ (2 n-2)(4 n-2) $$

Question

UpStudy AI · Accepted Answer

To find the product of $$ (2n - 2)(4n - 2) $$ and simplify the expression, follow these steps:

1. **Apply the Distributive Property (FOIL Method):**

$$
   (2n - 2)(4n - 2) = 2n \cdot 4n + 2n \cdot (-2) + (-2) \cdot 4n + (-2) \cdot (-2)
   $$

2. **Calculate Each Term:**

$$
   2n \cdot 4n = 8n^2
   $$
   $$
   2n \cdot (-2) = -4n
   $$
   $$
   (-2) \cdot 4n = -8n
   $$
   $$
   (-2) \cdot (-2) = 4
   $$

3. **Combine Like Terms:**

$$
   8n^2 - 4n - 8n + 4 = 8n^2 - 12n + 4
   $$

4. **Factor the Simplified Expression (Optional):**

You can factor out a **4** for further simplification:

$$
   8n^2 - 12n + 4 = 4(2n^2 - 3n + 1)
   $$
   
   Then, factor the quadratic:

$$
   2n^2 - 3n + 1 = (2n - 1)(n - 1)
   $$
   
   So, the fully factored form is:

$$
   4(2n - 1)(n - 1)
   $$

**Final Simplified Product:**

$$
8n^2 - 12n + 4
$$
The product of $$ (2n - 2)(4n - 2) $$ is $$ 8n^2 - 12n + 4 $$.

Find the product. Simplify your answer. \( (2 n-2)(4 n-2) \)