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प्रश्न
Simplify the following using the identities: \[\frac{198 \times 198 - 102 \times 102}{96}\]
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उत्तर
Let us consider the following expression: \[\frac{198 \times 198 - 102 \times 102}{96} = \frac{{198}^2 - {102}^2}{96}\]
Using the identity \[\left( a + b \right)\left( a - b \right) = a^2 - b^2\],we get:
\[\frac{198 \times 198 - 102 \times 102}{96} = \frac{{198}^2 - {102}^2}{96} = \frac{\left( 198 + 102 \right)\left( 198 - 102 \right)}{96}\]
\[\Rightarrow \frac{198 \times 198 - 102 \times 102}{96} = \frac{\left( 198 + 102 \right)\left( 198 - 102 \right)}{96}\]
\[ \Rightarrow \frac{198 \times 198 - 102 \times 102}{96} = \frac{300 \times 96}{96}\]
\[ \Rightarrow \frac{198 \times 198 - 102 \times 102}{96} = 300\]
Thus, the answer is 300.
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