Simplify 108 `xx` 109 = ?

Answer

To simplify \( 108 \times 109 \), we can use the distributive property of multiplication. Here’s the step-by-step solution:

### Step 1: Rewrite the numbers
We can express \( 108 \) and \( 109 \) in a more manageable form:
\[ 108 = 100 + 8 \]
\[ 109 = 100 + 9 \]

### Step 2: Apply the distributive property
Now, we can multiply these two expressions using the distributive property (also known as the FOIL method for binomials):
\[ (100 + 8)(100 + 9) \]

### Step 3: Multiply the terms
Now we will multiply each term:
1. \( 100 \times 100 = 10000 \)
2. \( 100 \times 9 = 900 \)
3. \( 8 \times 100 = 800 \)
4. \( 8 \times 9 = 72 \)

### Step 4: Add all the products together
Now, we sum all these products:
\[ 10000 + 900 + 800 + 72 \]

### Step 5: Perform the addition
Now, let's add these values step by step:
1. \( 10000 + 900 = 10900 \)
2. \( 10900 + 800 = 11700 \)
3. \( 11700 + 72 = 11772 \)

### Final Answer
Thus, the simplified result of \( 108 \times 109 \) is:
\[ \boxed{11772} \]