If a = 4011 and b = 3989 then value of ab = ?

Options

A. 15999879
B. 15899879
C. 15989979
D. 15998879

Answer

To find the value of \( ab \) where \( a = 4011 \) and \( b = 3989 \), we can use the difference of squares formula.

### Step-by-Step Solution:

1. **Rewrite the numbers**:
- We can express \( a \) and \( b \) in a more manageable form:
\[ a = 4011 = 4000 + 11 \]
\[ b = 3989 = 4000 - 11 \]

2. **Use the difference of squares formula**:
- The product \( ab \) can be rewritten using the identity \( (x+y)(x-y) = x^2 - y^2 \):
\[ ab = (4000 + 11)(4000 - 11) = 4000^2 - 11^2 \]

3. **Calculate \( 4000^2 \)**:
- We calculate \( 4000^2 \):
\[ 4000^2 = 16000000 \]

4. **Calculate \( 11^2 \)**:
- Now calculate \( 11^2 \):
\[ 11^2 = 121 \]

5. **Subtract the squares**:
- Now, we subtract \( 11^2 \) from \( 4000^2 \):
\[ ab = 16000000 - 121 = 15999879 \]

6. **Final Answer**:
- Therefore, the value of \( ab \) is:
\[ ab = 15999879 \]