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प्रश्न
Simplify the following using the formula: (a − b)(a + b) = a2 − b2: 197 × 203
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उत्तर
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 \[39991\].
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