If a=3 and b=-2, then `a^(2) + b^(2) + 2ab` =______

Options

A. 9
B. 4
C. 2
D. 1

Answer

To solve the expression \( a^2 + b^2 + 2ab \) given \( a = 3 \) and \( b = -2 \), we can follow these steps:

### Step 1: Substitute the values of \( a \) and \( b \)
We start by substituting \( a = 3 \) and \( b = -2 \) into the expression.

\[ a^2 + b^2 + 2ab = 3^2 + (-2)^2 + 2 \cdot 3 \cdot (-2) \]

### Step 2: Calculate \( a^2 \)
Now, calculate \( 3^2 \):

\[ 3^2 = 9 \]

### Step 3: Calculate \( b^2 \)
Next, calculate \( (-2)^2 \):

\[ (-2)^2 = 4 \]

### Step 4: Calculate \( 2ab \)
Now, calculate \( 2 \cdot 3 \cdot (-2) \):

\[ 2 \cdot 3 \cdot (-2) = 6 \cdot (-2) = -12 \]

### Step 5: Combine all the parts
Now, we can combine all the calculated parts:

\[ a^2 + b^2 + 2ab = 9 + 4 - 12 \]

### Step 6: Perform the addition and subtraction
Now, perform the addition and subtraction:

\[ 9 + 4 = 13 \]
\[ 13 - 12 = 1 \]

### Final Answer
Thus, the value of \( a^2 + b^2 + 2ab \) is:

\[ \boxed{1} \]

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