If `x=1.75, y = 0.5,` then find the value of `4x ^(2) + 4 xy + y ^(2) ?`

Options

A. `15.75`
B. `16.00`
C. `16.25`
D. `16.75`

Answer

To find the value of \( 4x^2 + 4xy + y^2 \) given \( x = 1.75 \) and \( y = 0.5 \), we can follow these steps:

### Step 1: Substitute the values of \( x \) and \( y \)
We start by substituting the values of \( x \) and \( y \) into the expression:

\[ 4x^2 + 4xy + y^2 = 4(1.75)^2 + 4(1.75)(0.5) + (0.5)^2 \]

### Step 2: Calculate \( 4x^2 \)
Now we calculate \( 4(1.75)^2 \):

\[ (1.75)^2 = 3.0625 \]
\[ 4(1.75)^2 = 4 \times 3.0625 = 12.25 \]

### Step 3: Calculate \( 4xy \)
Next, we calculate \( 4(1.75)(0.5) \):

\[ 4(1.75)(0.5) = 4 \times 1.75 \times 0.5 = 4 \times 0.875 = 3.5 \]

### Step 4: Calculate \( y^2 \)
Now we calculate \( (0.5)^2 \):

\[ (0.5)^2 = 0.25 \]

### Step 5: Combine all the results
Now we combine all the calculated values:

\[ 4x^2 + 4xy + y^2 = 12.25 + 3.5 + 0.25 \]

### Step 6: Final Calculation
Now we add these values together:

\[ 12.25 + 3.5 = 15.75 \]
\[ 15.75 + 0.25 = 16 \]

Thus, the final value of \( 4x^2 + 4xy + y^2 \) is \( 16 \).

### Final Answer:
\[ \text{The value of } 4x^2 + 4xy + y^2 \text{ is } 16. \]

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