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Q.

Without actually calculating the cubes, find the value of 0.2 3 − 0.3 3 + 0.1 3  .


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a

-0.018

b

-0.08

c

-0.8

d

0.018 

answer is A.

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Detailed Solution

Given expression is 0.2 3 − 0.3 3 + 0.1 3  .
First, in this procedure, check the values of a+b+c,   then if a+b+c=0,   it simplifies to a 3 + b 3 + c 3 =3abc  .
Here, in the given expression, we can observe that a+b+c=0.  
0.2−0.3+0.1=0.3−0.3=0  
Therefore, a 3 + b 3 + c 3 =3abc  
0.2 3 + −0.3 3 + 0.1 3 =3× 0.2 × −0.3 × 0.1                                           =−0.6×0.003                                           =−0.018.  
Therefore, the answer is −0.018.  
The correct option is (1).
 
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Without actually calculating the cubes, find the value of 0.2 3 − 0.3 3 + 0.1 3  .