Expand using suitable identities
$(x + 2 y + 4 z)^{2}$

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Solution

We need to expand $(x + 2 y + 4 z)^{2}$
We know appropriate identity $(x + y + z)^{2} = x^{2} + y^{2} + z^{2} + 2 x y + 2 y z + 2 x z$
Therefore, the value of $(x + 2 y + 4 z)^{2}$ is
$= x^{2} + (2 y)^{2} + (4 z)^{2} + 2 (x) (2 y) + 2 (2 y) (4 z) + 2 (x) (4 z)$
$= x^{2} + 4 y^{2} + 16 z^{2} + 4 x y + 16 y z + 8 x z$

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