Evaluate :
`xz(x^(2) + y^(2))` for x = 2, y = 1 and z = 1.

Answer

To evaluate the expression \( xz(x^2 + y^2) \) for \( x = 2 \), \( y = 1 \), and \( z = 1 \), we will follow these steps:

### Step 1: Substitute the values into the expression
We start with the expression:
\[ xz(x^2 + y^2) \]
Substituting \( x = 2 \), \( y = 1 \), and \( z = 1 \):
\[ 1 \cdot 2 \cdot (2^2 + 1^2) \]

### Step 2: Calculate \( x^2 \) and \( y^2 \)
Now, we calculate \( x^2 \) and \( y^2 \):
\[ x^2 = 2^2 = 4 \]
\[ y^2 = 1^2 = 1 \]

### Step 3: Add \( x^2 \) and \( y^2 \)
Next, we add \( x^2 \) and \( y^2 \):
\[ x^2 + y^2 = 4 + 1 = 5 \]

### Step 4: Multiply by \( x \) and \( z \)
Now, we multiply the result by \( x \) and \( z \):
\[ xz(x^2 + y^2) = 1 \cdot 2 \cdot 5 \]

### Step 5: Calculate the final result
Finally, we calculate:
\[ 1 \cdot 2 \cdot 5 = 10 \]

Thus, the final value of the expression \( xz(x^2 + y^2) \) is:
\[ \boxed{10} \]