Expand the following, using suitable identity.
$(a + 2 b + 4 c)^{2}$

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Solution

We have, $(a + 2 b + 4 c)^{2}$
$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$
$= (a)^{2} + (2 b)^{2} + (4 c)^{2} + 2 (a) (2 b) + 2 (2 b) (4 c) + 2 (a) (4 c)$
$= a^{2} + 4 b^{2} + 16 c^{2} + 4 a b + 16 b c + 8 a c$

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