Expand each of the following, using suitable identities:
$(x + 2 y + 4 z)^{2}$

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Solution

Given, $(x + 2 y + 4 y z)^{2}$

$= (A + B + C)^{2} = A^{2} + B^{2} + C^{2} + 2 a B + 2 B C + 2 C A$

$= (x^{2} + 4 y^{2} + 16 z^{2} + 4 x y + 16 y z + 8 z x)$

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