Simplify the expression and find its value when `a =5 and b=-3` then `2(a^2+ab)+3-ab`

Options

A. 36
B. 38
C. 30
D. 35

Explanation

To simplify the expression \( 2(a^2 + ab) + 3 - ab \) and find its value when \( a = 5 \) and \( b = -3 \), we will follow these steps:

### Step 1: Write down the expression
The expression we need to simplify is:
\[ 2(a^2 + ab) + 3 - ab \]

### Step 2: Substitute the values of \( a \) and \( b \)
We substitute \( a = 5 \) and \( b = -3 \) into the expression:
\[ 2(5^2 + 5 \cdot (-3)) + 3 - (5 \cdot (-3)) \]

### Step 3: Calculate \( 5^2 \) and \( 5 \cdot (-3) \)
Now, we calculate \( 5^2 \) and \( 5 \cdot (-3) \):
\[ 5^2 = 25 \]
\[ 5 \cdot (-3) = -15 \]

### Step 4: Substitute these values back into the expression
Now, substitute these values into the expression:
\[ 2(25 + (-15)) + 3 - (-15) \]

### Step 5: Simplify inside the parentheses
Now simplify inside the parentheses:
\[ 25 + (-15) = 25 - 15 = 10 \]
So the expression now becomes:
\[ 2(10) + 3 + 15 \]

### Step 6: Multiply and add
Now, multiply \( 2 \) by \( 10 \):
\[ 2 \cdot 10 = 20 \]
Now add \( 3 \) and \( 15 \):
\[ 20 + 3 + 15 \]

### Step 7: Final addition
Now, perform the final addition:
\[ 20 + 3 = 23 \]
\[ 23 + 15 = 38 \]

### Final Answer
The value of the expression when \( a = 5 \) and \( b = -3 \) is:
\[ \boxed{38} \]