A) \[(1+a)(1+b)(1+c)\]
B) \[(a+b+c+1)(a-b-c)\]
C) \[(a+b)(b+c)(c+a)\]
D) \[({{a}^{2}}+{{b}^{2}}+{{c}^{2}})(1-a-b-c)\]
Correct Answer: A
Solution :
\[1+a+b+c+ab+bc+ca+abc\] \[=(1+a)+(b+ab)+(c+ac)+(bc+abc)\] \[=1(1+a)+b(1+a)+c(1+a)+bc(1+a)\] \[=(1+a)(1+b+c+bc)\] \[=(1+a)[1(1+b)+c(1+b)]\] \[=(1+a)(1+b)(1+c)\]
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