Evaluate `x^3+y^3+z^3-3xyz` when x=2, y=-1 and z=3.

Answer

To evaluate the expression \( x^3 + y^3 + z^3 - 3xyz \) when \( x = 2 \), \( y = -1 \), and \( z = 3 \), we will substitute the values of \( x \), \( y \), and \( z \) into the expression step by step.

### Step 1: Substitute the values into the expression
We start with the expression:
\[ x^3 + y^3 + z^3 - 3xyz \]
Now, substitute \( x = 2 \), \( y = -1 \), and \( z = 3 \):
\[ (2)^3 + (-1)^3 + (3)^3 - 3(2)(-1)(3) \]

### Step 2: Calculate each term
Now we will calculate each term:
1. Calculate \( (2)^3 \):
\[ (2)^3 = 8 \]
2. Calculate \( (-1)^3 \):
\[ (-1)^3 = -1 \]
3. Calculate \( (3)^3 \):
\[ (3)^3 = 27 \]
4. Calculate \( 3(2)(-1)(3) \):
\[ 3(2)(-1)(3) = 3 \times 2 \times -1 \times 3 = -18 \]

### Step 3: Substitute the calculated values back into the expression
Now, substitute these calculated values back into the expression:
\[ 8 + (-1) + 27 - (-18) \]

### Step 4: Simplify the expression
Now, simplify the expression step by step:
1. Combine \( 8 \) and \( -1 \):
\[ 8 - 1 = 7 \]
2. Add \( 27 \):
\[ 7 + 27 = 34 \]
3. Subtract \( -18 \) (which is the same as adding \( 18 \)):
\[ 34 + 18 = 52 \]

### Final Result
Thus, the final value of the expression \( x^3 + y^3 + z^3 - 3xyz \) when \( x = 2 \), \( y = -1 \), and \( z = 3 \) is:
\[ \boxed{52} \]