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Simplify the Following Using the Identities: 198 × 198 − 102 × 102 96 - Mathematics

Answer in Brief

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

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Solution

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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APPEARS IN

RD Sharma Class 8 Maths
Chapter 6 Algebraic Expressions and Identities
Exercise 6.6 | Q 5.3 | Page 43
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