If ` x = 93, y = 93, z = 94 `then the value of ` ( x^(2) - y^(2)+ 10 xz + 10 yz)` is

Options

A. 104784
B. 147840
C. 174840
D. 184740

Answer

To solve the expression \( x^2 - y^2 + 10xz + 10yz \) given the values \( x = 93 \), \( y = 93 \), and \( z = 94 \), we can follow these steps:

### Step 1: Substitute the values of \( x \), \( y \), and \( z \)
We start by substituting the values into the expression:
\[ x^2 - y^2 + 10xz + 10yz = 93^2 - 93^2 + 10 \cdot 93 \cdot 94 + 10 \cdot 93 \cdot 94 \]

### Step 2: Simplify \( x^2 - y^2 \)
Since \( x \) and \( y \) are equal, we have:
\[ 93^2 - 93^2 = 0 \]
Thus, the expression simplifies to:
\[ 0 + 10 \cdot 93 \cdot 94 + 10 \cdot 93 \cdot 94 \]

### Step 3: Combine the terms
Now, we can combine the two identical terms:
\[ 10 \cdot 93 \cdot 94 + 10 \cdot 93 \cdot 94 = 20 \cdot 93 \cdot 94 \]

### Step 4: Calculate \( 20 \cdot 93 \cdot 94 \)
Now we need to calculate \( 20 \cdot 93 \cdot 94 \):
\[ 20 \cdot 93 \cdot 94 = 20 \cdot (93 \cdot 94) \]
First, calculate \( 93 \cdot 94 \):
\[ 93 \cdot 94 = 8742 \]
Now multiply by 20:
\[ 20 \cdot 8742 = 174840 \]

### Final Result
Thus, the value of the expression \( x^2 - y^2 + 10xz + 10yz \) is:
\[ \boxed{174840} \]