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Question

Expansion of a3+b3+c33abc is


A
12(a+b+c)×((ab)2+(bc)2+(ca)2)
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B
(a+b+c)×(a2+b2+c2abbcca)
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C
Both (A) & (B)
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D
None of the above
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Solution

The correct option is D Both (A) & (B)
a3+b3+c33abc=(a+b+c)×(a2+b2+c2abbcca)

=12(a+b+c)×(2a2+2b2+2c22ab2bc2ca)

=12(a+b+c)×[a2+b22ab+b2+c22bc+c2+a22ca]

=12(a+b+c)×[(a2+b22ab)+(b2+c22bc)+(c2+a22ca)]

=12(a+b+c)×[(ab)2+(bc)2+(ca)2]

 

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