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Question

Expansion of a3+b3+c33abc is


  1. (a+b+c)(a2+b2+c2abbcca)

  2. \N
  3. \N
  4. 12(a+b+c)((ab)2+(bc)2+(ca)2)


Solution

The correct option is B \N

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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