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Question
Write in the expanded form: (ab + bc + ca)2
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Solution
We have
(ab + bc + ca)2 = (ab)2 + (bc)2 + (ca )2 + 2 (ab)(bc) + 2(bc)ca + 2 (ab)(ca )
[∵ (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca]
= a2b2 + b2c2 + c2a2 + 2ab2c + 2bc2a + 2a2bc
∴ (ab + bc + ca)2 = a2b2 + b2c2 + c2a2 + 2ab2c + 2bc2a + 2a2bc
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