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प्रश्न
Simplify the following using the formula: (a − b)(a + b) = a2 − b2: 95 × 105
उत्तर
Here, we will use the identity \[(a - b)(a + b) = a^2 - b^2\]
Let us consider the following product: \[95 \times 105\]
\[\because \frac{95 + 105}{2} = \frac{200}{2} = 100\];therefore, we will write the above product as:
\[95 \times 105\]
\[ = \left( 100 + 5 \right)\left( 100 - 5 \right)\]
\[ = \left( 100 \right)^2 - \left( 5 \right)^2 \]
\[ = 10000 - 25\]
\[ = 9975\]
Thus, the answer is 9975.
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