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 can follow these steps:

### Step 1: Expand the expression
We start with the expression:
\[ 2(a^2 + ab) + 3 - ab \]
Distributing \( 2 \) into the parentheses:
\[ = 2a^2 + 2ab + 3 - ab \]

### Step 2: Combine like terms
Next, we combine the like terms \( 2ab \) and \( -ab \):
\[ = 2a^2 + (2ab - ab) + 3 \]
This simplifies to:
\[ = 2a^2 + ab + 3 \]

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

### Step 4: Calculate \( 5^2 \)
Calculating \( 5^2 \):
\[ = 2(25) + (5)(-3) + 3 \]

### Step 5: Multiply the terms
Now, we multiply:
\[ = 50 - 15 + 3 \]

### Step 6: Perform the addition and subtraction
Finally, we perform the addition and subtraction:
\[ = 50 - 15 = 35 \]
Then,
\[ = 35 + 3 = 38 \]

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