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a) 97^2 = (90+7)^2 = 90^2 + 2×90×7 + 7^2 = 8100 + 1260 + 49 = 9409.
Note :- 1st question was solved using identity:- (a+b)^2 = a^2 + 2ab + b^2
b) Using the identity (x+a)(x+b) = x2+(a+b)x+ab
Writing 102 as 100+2 and 98 as 100−2
Hence (100+2)(100−2) = 1002+[2+(−2)]100+(2)(−2)
= 10000+(0)100−4
= 9996
The answer is 9996
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Answer:
(a) 97²
(100 - 3)²
(a - b)² = a²+b²-2ab
(100 - 3)² = (100)²+(3)²-2×100×3
= 10000+9-600
= 10009-600
= 9409
(b) 101×98
(100+1) × (100-2)
(x+a) (x+b) = x²+(a+b)x+ab
= (100)²+(1-2)100+1×-2
= 10000-100-2
= 10000-102
= 9898
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