Explanation:
Taking LHS of the identity:
(a + b +c)2
This can also be written as:
= (a + b + c) (a + b + c)
Multiply as we do multiplication of trinomials and we get:
= a(a + b + c) + b(a + b + c) + c(a + b + c)
= a2 + ab + ac + ab + b2 + bc + ac + bc + c2
Rearrange the terms and we get:
= a2 + b2 + c2 + ab + ab + bc + bc + ac + ac
Add like terms and we get:
= a2 + b2+ c2 + 2ab + 2bc + 2ca
Hence, in this way we obtain the identity i.e. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca