Factorise $a^{2} + b^{2} + 2ab + 2bc + 2ca$.

Factorise $a^{2} + b^{2} + 2ab + 2bc + 2ca$.
  1. $(a + b + c)^{2} - c^{2}$
  2. $(a + b)(a + b + 2c)$
  3. $(a + b + c)^{2}$
  4. $(a - b + c)^{2}$

Solution

Group: $(a^{2}+2ab+b^{2}) + 2c(a+b) = (a+b)^{2}+2c(a+b) = (a+b)(a+b+2c)$.

Asked in: IMO

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