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Question

Show that : [a+bb+cc+a]=2[abc].

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Solution

[a+bb+cc+a]
=(a+b).[(b+c)×(c+a)]
=(a+b).[(b×c)+(b×a)+(c×c)+(c×a)]
=(a+b).[(b×c)+(b×a)+(c×a)]
={a.(b×c)}+{a.(b×a)}+{a.(c×a)}+{b.(b×c)}+{b.(b×a)}+{b.(c×a)}
=[abc]+[aba]+[aca][bbc]+[bba]+[bca]
=[abc]+[bca]=2[abc]

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