Using suitable identity, evaluate:
`(104)^(3)`

Answer

To evaluate \( (104)^3 \) using a suitable identity, we can follow these steps:

### Step 1: Rewrite the expression
We can express \( 104 \) as \( 100 + 4 \). Therefore, we rewrite the expression as:
\[ (104)^3 = (100 + 4)^3 \]

### Step 2: Apply the identity
We will use the binomial expansion formula for \( (x + y)^3 \), which is given by:
\[ (x + y)^3 = x^3 + y^3 + 3x^2y + 3xy^2 \]
In our case, \( x = 100 \) and \( y = 4 \).

### Step 3: Calculate each term
1. Calculate \( x^3 \):
\[ 100^3 = 1000000 \]
2. Calculate \( y^3 \):
\[ 4^3 = 64 \]
3. Calculate \( 3x^2y \):
\[ 3 \cdot (100^2) \cdot 4 = 3 \cdot 10000 \cdot 4 = 120000 \]
4. Calculate \( 3xy^2 \):
\[ 3 \cdot 100 \cdot (4^2) = 3 \cdot 100 \cdot 16 = 4800 \]

### Step 4: Combine all the terms
Now we add all the calculated terms together:
\[ 1000000 + 64 + 120000 + 4800 \]

### Step 5: Perform the addition
1. First, add \( 1000000 + 120000 \):
\[ 1000000 + 120000 = 1120000 \]
2. Next, add \( 1120000 + 4800 \):
\[ 1120000 + 4800 = 1124800 \]
3. Finally, add \( 1124800 + 64 \):
\[ 1124800 + 64 = 1124864 \]

Thus, the final result is:
\[ (104)^3 = 1124864 \]