Using identify, find the value of `(-7)^(3)+(5)^(3)+(2)^(3)`.

Answer

To solve the problem using the identity for the sum of cubes, we will follow these steps:

### Step 1: Identify the values
We are given the expression \((-7)^3 + (5)^3 + (2)^3\). Let's denote:
- \(x = -7\)
- \(y = 5\)
- \(z = 2\)

### Step 2: Check the sum
We need to check if \(x + y + z = 0\):
\[ x + y + z = -7 + 5 + 2 \]
Calculating this gives:
\[ -7 + 5 = -2 \]
\[ -2 + 2 = 0 \]
Thus, \(x + y + z = 0\).

### Step 3: Apply the identity
According to the identity:
\[ x^3 + y^3 + z^3 = 3xyz \quad \text{(if } x + y + z = 0\text{)} \]
We can now substitute \(x\), \(y\), and \(z\) into the identity:
\[ (-7)^3 + (5)^3 + (2)^3 = 3 \cdot (-7) \cdot 5 \cdot 2 \]

### Step 4: Calculate \(xyz\)
Now we calculate \(xyz\):
\[ xyz = (-7) \cdot 5 \cdot 2 \]
Calculating this step-by-step:
\[ (-7) \cdot 5 = -35 \]
\[ -35 \cdot 2 = -70 \]
So, \(xyz = -70\).

### Step 5: Substitute back into the identity
Now substituting back into the identity:
\[ (-7)^3 + (5)^3 + (2)^3 = 3 \cdot (-70) \]
Calculating this gives:
\[ 3 \cdot (-70) = -210 \]

### Final Answer
Thus, the value of \((-7)^3 + (5)^3 + (2)^3\) is:
\[ \boxed{-210} \]