Use (a – b)2 = a2 – 2ab – b2 to evaluate the following:
(i) (99)2
(ii) (997)2
(iii) (9.8)2
Answer :
(i) (99)2
It can be written as
= (100 – 1)2
Expanding using formula
= 1002 – 2 × 100 × 1 + 12
By further calculation
= 10000 – 200 + 1
= 9801
(ii) (997)2
It can be written as
= (1000 – 3)2
Expanding using formula
= 10002 – 2 × 1000 × 3 + 32
By further calculation
= 1000000 – 6000 + 9
= 994009
(iii) (9.8)2
It can be written as
= (10 – 0.2)2
Expanding using formula
= 102 – 2 × 10 × 0.2 + 0.22
By further calculation
= 100 – 4 + 0.04
= 96.04
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