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Question

Find the value of: ∣∣ ∣∣b+ca+bac+ab+cba+bc+ac∣∣ ∣∣

A
a3+b3+c3
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B
3abc
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C
a3+b3+c33abc
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D
a2+b2+c2abbcca
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Solution

The correct option is C a3+b3+c33abc
Let A=∣ ∣b+ca+bac+ab+cba+bc+ac∣ ∣

Performing C2C2C3
A=∣ ∣b+cbac+acba+bac∣ ∣
Performing C1C1C2
A=∣ ∣cbaacbbac∣ ∣
A=c(c2ab)b(acb2)+a(a2bc)
A=c3abcbac+b3+a3abc

A=a3+b3+c33abc

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