Express each of the following in factors form,
` ( 5x- 3y ) ^(3)+ (3y - 8z)^(3) + (8z - 5x) ^(3)`

Answer

To express the given expression \( (5x - 3y)^3 + (3y - 8z)^3 + (8z - 5x)^3 \) in factor form, we can use the identity for the sum of cubes.

### Step-by-Step Solution:

1. **Identify the terms**: Let
\[ a = 5x - 3y, \quad b = 3y - 8z, \quad c = 8z - 5x. \]
We need to express \( a^3 + b^3 + c^3 \).

2. **Check the condition**: We need to check if \( a + b + c = 0 \):
\[ a + b + c = (5x - 3y) + (3y - 8z) + (8z - 5x). \]
Simplifying this:
\[ = 5x - 3y + 3y - 8z + 8z - 5x = 0. \]
Thus, \( a + b + c = 0 \).

3. **Use the identity**: Since \( a + b + c = 0 \), we can use the identity:
\[ a^3 + b^3 + c^3 = 3abc. \]

4. **Calculate \( abc \)**:
\[ abc = (5x - 3y)(3y - 8z)(8z - 5x). \]

5. **Final expression**: Therefore, we can express the original expression as:
\[ (5x - 3y)^3 + (3y - 8z)^3 + (8z - 5x)^3 = 3(5x - 3y)(3y - 8z)(8z - 5x). \]

### Final Answer:
\[ (5x - 3y)^3 + (3y - 8z)^3 + (8z - 5x)^3 = 3(5x - 3y)(3y - 8z)(8z - 5x). \]