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Q.

Evaluate: (202) 2 + (198) 2  


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a

80008

b

808

c

88

d

8008 

answer is A.

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Detailed Solution

Given expression: (202) 2 + (198) 2  .
Rewrite 202=200+2 and 198=200-2.
(202) 2 + (198) 2 = (200+2) 2 + (200−2) 2  
Apply identities,
  x+y 2 = x 2 +2xy+ y 2 , x−y 2 = x 2 −2xy+ y 2   where x=200 and y =2.
  (202) 2 + (198) 2 = 200 2 +2×200×2+ 2 2 + 200 2 −2×200×2+ 2 2  
Cancel 2 ×  200 ×  2,
Simplify remaining terms and add them all.
(202) 2 + (198) 2 =40000+4+40000+4 ⇒ (202) 2 + (198) 2 =80008  
(202) 2 + (198) 2 =80008  .
Hence, option 1 is correct.
 
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