If p = 4,q = -3 and r = 2, find the value of `: p^(3)+q^(3)-r^(3)-3pqr`

Answer

To solve the expression \( p^3 + q^3 - r^3 - 3pqr \) given \( p = 4 \), \( q = -3 \), and \( r = 2 \), we will follow these steps:

### Step 1: Substitute the values of p, q, and r into the expression.
We start with the expression:
\[ p^3 + q^3 - r^3 - 3pqr \]
Substituting the values:
\[ 4^3 + (-3)^3 - 2^3 - 3 \cdot 4 \cdot (-3) \cdot 2 \]

### Step 2: Calculate each term.
Now we calculate each term separately:
- \( 4^3 = 64 \)
- \( (-3)^3 = -27 \)
- \( 2^3 = 8 \)
- \( 3 \cdot 4 \cdot (-3) \cdot 2 = 3 \cdot 4 \cdot -3 \cdot 2 = -72 \)

### Step 3: Substitute the calculated values back into the expression.
Now we substitute these calculated values back into the expression:
\[ 64 + (-27) - 8 - (-72) \]

### Step 4: Simplify the expression.
Now, we simplify the expression step-by-step:
1. Start with \( 64 - 27 = 37 \)
2. Then, \( 37 - 8 = 29 \)
3. Finally, \( 29 + 72 = 101 \)

### Final Answer
Thus, the value of the expression \( p^3 + q^3 - r^3 - 3pqr \) is:
\[ \boxed{101} \]