Find the value of the expressions, when `a= -1" and "b= 3`
`a^(2)+b^(2)+2ab`

Answer

To find the value of the expression \( a^2 + b^2 + 2ab \) when \( a = -1 \) and \( b = 3 \), we will follow these steps:

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

\[ (-1)^2 + (3)^2 + 2(-1)(3) \]

### Step 2: Calculate \( (-1)^2 \)
Next, we calculate \( (-1)^2 \):

\[ (-1)^2 = 1 \]

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

\[ (3)^2 = 9 \]

### Step 4: Calculate \( 2(-1)(3) \)
Now we calculate \( 2(-1)(3) \):

\[ 2(-1)(3) = -6 \]

### Step 5: Combine all the results
Now we combine all the results from the previous steps:

\[ 1 + 9 - 6 \]

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

\[ 1 + 9 = 10 \]
\[ 10 - 6 = 4 \]

### Final Answer
Thus, the value of the expression \( a^2 + b^2 + 2ab \) when \( a = -1 \) and \( b = 3 \) is:

\[ \boxed{4} \]