Find the cube of 35.

Answer

To find the cube of 35, we can use the identity for the cube of a binomial, which states that:

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

In this case, we can express 35 as \(30 + 5\). Therefore, we need to calculate \((30 + 5)^3\).

### Step-by-Step Solution:

1. **Identify \(a\) and \(b\)**:
- Let \(a = 30\) and \(b = 5\).

2. **Apply the binomial cube formula**:
- Using the formula:
\[ (a + b)^3 = a^3 + b^3 + 3ab(a + b) \]

3. **Calculate \(a^3\)**:
- \(a^3 = 30^3 = 27000\).

4. **Calculate \(b^3\)**:
- \(b^3 = 5^3 = 125\).

5. **Calculate \(3ab\)**:
- \(3ab = 3 \times 30 \times 5 = 450\).

6. **Calculate \(3ab(a + b)\)**:
- \(3ab(a + b) = 450 \times (30 + 5) = 450 \times 35 = 15750\).

7. **Combine all the parts**:
- Now, add all the components together:
\[ (30 + 5)^3 = 27000 + 125 + 15750 \]

8. **Perform the final addition**:
- \(27000 + 125 = 27125\)
- \(27125 + 15750 = 42875\)

Thus, the cube of 35 is:

\[ \boxed{42875} \]