Question

Simplify the following using the formula: (a − b)(a + b) = a² − b²: 197 × 203

Answer 1

Here, we will use the identity  \[(a - b)(a + b) = a^2 - b^2\]

Let us consider the following product: \[197 \times 203\] 

\[\because \frac{197 + 203}{2} = \frac{400}{2} = 200\];  therefore, we will write the above product as:

\[197 \times 203\]

\[ = \left( 200 - 3 \right)\left( 200 + 3 \right)\]

\[ = \left( 200 \right)^2 - \left( 3 \right)^2 \]

\[ = 40000 - 9\]

\[ = 39991\]

Thus, the answer is \[39991\].