Mutiply 125 by 125.

Answer

To multiply 125 by 125 using a shortcut method, we can break down the numbers into simpler components. Here’s a step-by-step solution:

### Step 1: Break down 125
We can express 125 as the sum of 100 and 25:
\[ 125 = 100 + 25 \]

### Step 2: Set up the multiplication
Now, we can write the multiplication as:
\[ 125 \times 125 = (100 + 25) \times (100 + 25) \]

### Step 3: Apply the distributive property
Using the distributive property (also known as the FOIL method for binomials), we can expand the expression:
\[ (100 + 25)(100 + 25) = 100 \times 100 + 100 \times 25 + 25 \times 100 + 25 \times 25 \]

### Step 4: Calculate each term
Now, we calculate each of the terms:
1. \( 100 \times 100 = 10000 \)
2. \( 100 \times 25 = 2500 \)
3. \( 25 \times 100 = 2500 \)
4. \( 25 \times 25 = 625 \)

### Step 5: Add the results
Now, we add all these results together:
\[ 10000 + 2500 + 2500 + 625 \]

Calculating this step-by-step:
1. \( 10000 + 2500 = 12500 \)
2. \( 12500 + 2500 = 15000 \)
3. \( 15000 + 625 = 15625 \)

### Final Result
Thus, the product of \( 125 \times 125 \) is:
\[ \boxed{15625} \]

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