Evaluate : and write the answer in factors form :
` (3a- 2b)^(3) + (2b- 5c)^(3) + (5c- 3a) ^(3)`

Answer

To evaluate the expression \( (3a - 2b)^3 + (2b - 5c)^3 + (5c - 3a)^3 \) and write the answer in factor form, we can use the identity for the sum of cubes.

### Step-by-Step Solution:

1. **Identify the terms**: We have three terms in the expression:
- Let \( x = 3a - 2b \)
- Let \( y = 2b - 5c \)
- Let \( z = 5c - 3a \)

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

3. **Apply the identity**: The identity states that if \( x + y + z = 0 \), then:
\[ x^3 + y^3 + z^3 = 3xyz \]
Therefore, we can write:
\[ (3a - 2b)^3 + (2b - 5c)^3 + (5c - 3a)^3 = 3(3a - 2b)(2b - 5c)(5c - 3a) \]

4. **Final answer in factor form**: Thus, the expression can be written as:
\[ 3(3a - 2b)(2b - 5c)(5c - 3a) \]

### Final Answer:
\[ (3a - 2b)^3 + (2b - 5c)^3 + (5c - 3a)^3 = 3(3a - 2b)(2b - 5c)(5c - 3a) \]