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It's easy to evalute (a + b + c)2.....
Let x = (a + b)....then expand (x + c)2 as you would normally in the case of binomial expansion......which is :
(x + c)2 = x2 + c2 + 2xc ......(1)
Now, replace x with (a + b) in (1).....then it becomes.......
(a + b)2 + c2 + 2.(a + b).c .....(2)
Just a little more to be done here ( now we expand (2) in the last step)........
a2 + b2 + 2ab + c2 + 2ac + 2bc (rearranging this we get)
a2 + b2 + c2 + 2ab + 2bc + 2ac .
this happens to be the expansion for (a + b = c)2
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