FOIL `(sqrt8-sqrt2)(sqrt8-sqrt2)`

Answer

To solve the expression \((\sqrt{8} - \sqrt{2})(\sqrt{8} - \sqrt{2})\) using the FOIL method, we will follow these steps:

### Step 1: Identify the terms
In the expression \((\sqrt{8} - \sqrt{2})(\sqrt{8} - \sqrt{2})\), we have:
- First term (F): \(\sqrt{8}\)
- Outside term (O): \(-\sqrt{2}\)
- Inside term (I): \(-\sqrt{2}\)
- Last term (L): \(-\sqrt{2}\)

### Step 2: Apply the FOIL method
Using the FOIL method, we calculate each part:

1. **First (F)**:
\[ \sqrt{8} \cdot \sqrt{8} = 8 \]

2. **Outside (O)**:
\[ \sqrt{8} \cdot (-\sqrt{2}) = -\sqrt{16} = -4 \]

3. **Inside (I)**:
\[ (-\sqrt{2}) \cdot \sqrt{8} = -\sqrt{16} = -4 \]

4. **Last (L)**:
\[ (-\sqrt{2}) \cdot (-\sqrt{2}) = \sqrt{4} = 2 \]

### Step 3: Combine all parts
Now, we combine all the results from the FOIL method:
\[ 8 + (-4) + (-4) + 2 \]

### Step 4: Simplify the expression
Now, we simplify the expression:
\[ 8 - 4 - 4 + 2 = 8 - 8 + 2 = 0 + 2 = 2 \]

### Final Answer
Thus, the result of \((\sqrt{8} - \sqrt{2})(\sqrt{8} - \sqrt{2})\) is:
\[ \boxed{2} \]