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Solve the expression using identities $198 × 198 − 102 × 102 96$ .

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300

320

200

120

answer is A.

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Detailed Solution

Given expression is

198 × 198 − 102 × 102 96

.
Using the identity,

a + b a − b = a 2 − b 2

Consider, a=198 and b=102.

198 × 198 − 102 × 102 96 = 1982 − 1022 96 ⇒ 198 × 198 − 102 × 102 96 = 198 + 102 198 − 102 96 ⇒ 198 × 198 − 102 × 102 96 = 300 × 96 96 ⇒ 198 × 198 − 102 × 102 96 = 300

So, the value of

198 × 198 − 102 × 102 96

is 300.
Hence, option 1 is correct.

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