Question

Simplify the following using the identities: \[\frac{198 \times 198 - 102 \times 102}{96}\]

Answer 1

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.