The cube of 105 is

Options

A. 1157625
B. 1175625
C. 1185625
D. 1158625

Answer

To find the cube of 105, we can use the formula for the cube of a binomial, which is:

\[ (a + b)^3 = a^3 + b^3 + 3a^2b + 3ab^2 \]

In this case, we can let \( a = 100 \) and \( b = 5 \). Therefore, we can express 105 as \( 100 + 5 \).

### Step 1: Identify \( a \) and \( b \)
Let:
- \( a = 100 \)
- \( b = 5 \)

### Step 2: Apply the binomial cube formula
Using the formula:
\[ (100 + 5)^3 = 100^3 + 5^3 + 3(100^2)(5) + 3(100)(5^2) \]

### Step 3: Calculate \( a^3 \) and \( b^3 \)
- \( a^3 = 100^3 = 1000000 \)
- \( b^3 = 5^3 = 125 \)

### Step 4: Calculate \( 3a^2b \)
- \( 3a^2b = 3 \times (100^2) \times 5 = 3 \times 10000 \times 5 = 150000 \)

### Step 5: Calculate \( 3ab^2 \)
- \( 3ab^2 = 3 \times 100 \times (5^2) = 3 \times 100 \times 25 = 7500 \)

### Step 6: Combine all the parts
Now, we can combine all these values:
\[ 1000000 + 125 + 150000 + 7500 \]

### Step 7: Perform the addition
Calculating step by step:
1. \( 1000000 + 125 = 1000125 \)
2. \( 1000125 + 150000 = 1150125 \)
3. \( 1150125 + 7500 = 1157625 \)

### Final Answer
Thus, the cube of 105 is:
\[ \boxed{1157625} \]