When x=4 and y=2 find the value of :
`x^(2)-2xy+y^(2)`

Options

A. 4
B. 6
C. 8
D. 10

Answer

To find the value of the expression \( x^2 - 2xy + y^2 \) when \( x = 4 \) and \( y = 2 \), we can follow these steps:

### Step 1: Write down the expression
The expression we need to evaluate is:
\[ x^2 - 2xy + y^2 \]

### Step 2: Substitute the values of \( x \) and \( y \)
We substitute \( x = 4 \) and \( y = 2 \) into the expression:
\[ (4)^2 - 2(4)(2) + (2)^2 \]

### Step 3: Calculate \( x^2 \)
Calculate \( (4)^2 \):
\[ (4)^2 = 16 \]

### Step 4: Calculate \( -2xy \)
Calculate \( -2(4)(2) \):
\[ -2(4)(2) = -16 \]

### Step 5: Calculate \( y^2 \)
Calculate \( (2)^2 \):
\[ (2)^2 = 4 \]

### Step 6: Combine the results
Now, we combine all the calculated values:
\[ 16 - 16 + 4 \]

### Step 7: Simplify the expression
Now, simplify:
\[ 16 - 16 = 0 \]
So, we have:
\[ 0 + 4 = 4 \]

### Final Answer
Thus, the value of the expression \( x^2 - 2xy + y^2 \) when \( x = 4 \) and \( y = 2 \) is:
\[ \boxed{4} \]