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Question

If a+b+c=0, then the value of (a+bc)3+(b+ca)3+(c+ab)3 is:


A

8(a3+b3+c3)

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B

a3+b3+c3

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C

24 abc

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D

24 abc

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Solution

The correct option is D

24 abc


a+b+c=0
Now, (a+bc)3=(a+b+ccc)3
=(02c)3=8c3
(b+ca)3=(b+c+aaa)3
=(02a)3=8a3
(c+ab)3=(c+a+bbb)3
=(02b)3=8b3
(a+bc)3+(b+ca)3+(c+ab)3
=(8c3)+(8a3)+(8b3)
=8(a3+b3+c3)=8(3abc)=24abc....... using :[a3+b3+c33abc
=(a+b+c)(a2+b2+c2abbcca)]
[If a+b+c=0 then a3+b3+c3=3abc]


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