Use (a + b)2 = a2 + 2ab + b2 to evaluate the following:
(i) (101)2
(ii) (1003)2
(iii) (10.2)2
Answer :
(i) (101)2
It can be written as
= (100 + 1)2
Expanding using formula
= 1002 + 12 + 2 × 100 × 1
By further calculation
= 10000 + 1 + 200
= 10201
(ii) (1003)2
It can be written as
= (1000 + 3)2
Expanding using formula
= 10002 + 32 + 2 × 1000 × 3
By further calculation
= 1000000 + 9 + 6000
= 1006009
(iii) (10.2)2
It can be written as
= (10 + 0.2)2
Expanding using formula
= 102 + 0.22 + 2 × 10 × 0.2
By further calculation
= 100 + 0.04 + 4
= 104.04
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