If a and b are odd numbers, then which of the following is even ?

Options

A. `a+b+ab`
B. `a+b-2`
C. `a+b+1`
D. `a+b+2ab`

Answer

To determine which of the given expressions is even when \( a \) and \( b \) are odd numbers, we will evaluate each option step by step.

### Step 1: Define odd numbers
Let’s define two odd numbers:
- Let \( a = 3 \)
- Let \( b = 5 \)

### Step 2: Evaluate each option

#### Option 1: \( a + b + ab \)
- Calculate \( a + b \):
\[ a + b = 3 + 5 = 8 \]
- Calculate \( ab \):
\[ ab = 3 \times 5 = 15 \]
- Now, combine these results:
\[ a + b + ab = 8 + 15 = 23 \]
- Since 23 is odd, this option is **not even**.

#### Option 2: \( a + b - 2 \)
- We already calculated \( a + b = 8 \).
- Now, subtract 2:
\[ a + b - 2 = 8 - 2 = 6 \]
- Since 6 is even, this option is **even**.

#### Option 3: \( a + b + 1 \)
- Using \( a + b = 8 \):
\[ a + b + 1 = 8 + 1 = 9 \]
- Since 9 is odd, this option is **not even**.

#### Option 4: \( a + b + 2ab \)
- We already calculated \( a + b = 8 \) and \( ab = 15 \).
- Now calculate \( 2ab \):
\[ 2ab = 2 \times 15 = 30 \]
- Combine these results:
\[ a + b + 2ab = 8 + 30 = 38 \]
- Since 38 is even, this option is **even**.

### Conclusion
From the evaluations:
- Option 1: Odd
- Option 2: Even
- Option 3: Odd
- Option 4: Even

Thus, the expressions that yield even results are:
- \( a + b - 2 \)
- \( a + b + 2ab \)