Use property to evaluate:
`38^(3) + (-26)^(3) + (-12)^(3)`

Answer

To evaluate the expression \( 38^3 + (-26)^3 + (-12)^3 \) using properties of cubes, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the values:**
Let \( A = 38 \), \( B = -26 \), and \( C = -12 \).

2. **Calculate \( A + B + C \):**
\[ A + B + C = 38 + (-26) + (-12) = 38 - 26 - 12 = 38 - 38 = 0 \]

3. **Apply the property of cubes:**
Since \( A + B + C = 0 \), we can use the identity:
\[ A^3 + B^3 + C^3 = 3ABC \]

4. **Calculate \( ABC \):**
\[ ABC = 38 \times (-26) \times (-12) \]
First, calculate \( (-26) \times (-12) \):
\[ (-26) \times (-12) = 312 \]
Now, calculate \( 38 \times 312 \):
\[ 38 \times 312 = 38 \times (300 + 12) = 38 \times 300 + 38 \times 12 \]
\[ 38 \times 300 = 11400 \]
\[ 38 \times 12 = 456 \]
\[ 38 \times 312 = 11400 + 456 = 11856 \]

5. **Calculate \( 3ABC \):**
\[ 3ABC = 3 \times 11856 = 35568 \]

6. **Final Result:**
Therefore,
\[ 38^3 + (-26)^3 + (-12)^3 = 35568 \]