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Question

If A=a2abacabb2bcacbcc2 and a2+b2+c2=1, then A2=

A
A
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B
2A
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C
3A
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D
4A
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Solution

The correct option is A A
A2=a2abacabb2bcacbcc2a2abacabb2bcacbcc2

=a4+a2b2+a2c2a3b+ab3+abc2a3c+ab2c+ac3a3b+ab3+abc2a2b2+b4+b2c2a2bc+b3c+bc3a3c+b2ac+ac3a2bc+b3c+bc3a2c2+b2c2+c4
=⎢ ⎢a2(a2+b2+c2)ab(a2+b2+c2)ac(a2+b2+c2)ab(a2+b2+c2)b2(a2+b2+c2)bc(a2+b2+c2)ac(a2+b2+c2)bc(a2+b2+c2)c2(a2+b2+c2)⎥ ⎥
=a2abacabb2bcacbcc2=A (a2+b2+c2=1)

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