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Question

Simplify: a2(bc)2(a+c)2b2+b2(ac)2(a+b)2c2+c2(ab)2(b+c)2a2

A
1
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B
abc
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C
a+b+c
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D
0
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Solution

The correct option is A 1
Given, a2(bc)2(a+c)2b2+b2(ac)2(a+b)2c2+c2(ab)2(b+c)2a2

=(a+bc)(ab+c)(a+cb)(a+b+c)+(b+ac)(ba+c)(a+bc)(a+b+c)+(c+ab)(ca+b)(b+ca)(a+b+c)
=(a+bc)(a+b+c)+(ba+c)(a+b+c)+(c+ab)(a+b+c)=(a+bc)+(ba+c)+(ca+b)(a+b+c)
=a+b+c(a+b+c)=1

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