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Question
Factorize: a2 + b2 + 2 (ab + bc + ca)
Solution
= a2 + b2 + 2ab + 2bc + 2ca
Using identity a2 + b2 + 2ab = (a + b)2
We get,
= (a + b)2 + 2bc + 2ca
= (a + b)2 + 2c (b + a)
or (a + b)2 + 2c (a + b)
Taking (a + b) common
= (a + b)(a + b + 2c )
∴ a2 + b2 + 2 (ab + bc + ca) = (a + b)(a + b + 2c)
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