Find the product using distributive property of multiplication.
`354xx102`

Answer

To find the product of 354 and 102 using the distributive property of multiplication, we can follow these steps:

### Step 1: Break down the second number
We can express 102 as the sum of 100 and 2.
So, we write:
\[ 102 = 100 + 2 \]

### Step 2: Apply the distributive property
According to the distributive property, we can rewrite the multiplication as:
\[ 354 \times 102 = 354 \times (100 + 2) \]
Using the distributive property, this becomes:
\[ 354 \times 100 + 354 \times 2 \]

### Step 3: Calculate each part
Now, we calculate each part separately:
1. Calculate \( 354 \times 100 \):
\[ 354 \times 100 = 35400 \]

2. Calculate \( 354 \times 2 \):
\[ 354 \times 2 = 708 \]
(Here, \( 2 \times 4 = 8 \), \( 2 \times 5 = 10 \) (write 0, carry 1), \( 2 \times 3 = 6 + 1 = 7 \))

### Step 4: Add the results
Now, we add the two results together:
\[ 35400 + 708 \]

To add these:
- Align the numbers:
```
35400
+ 708
```
- Start adding from the right:
- 0 + 8 = 8
- 0 + 0 = 0
- 4 + 7 = 11 (write 1, carry 1)
- 5 + 1 (carry) = 6
- 3 + 0 = 3

So, the final sum is:
\[ 35400 + 708 = 36108 \]

### Final Answer
Thus, the product of 354 and 102 is:
\[ \boxed{36108} \]

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