Add: $2 x (z + x + y)$ and $2 y (z + y + x)$

2 x + 2 y + 4 x y + 2 y z + 2 z x

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2 x^{2} + 2 y^{2} + 4 x y + 2 y + 2 x

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2 x^{2} + 2 y^{2} + 4 x y + 2 y z + 2 z x

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2 x^{2} + 2 y^{2} + 4 x^{2} y^{2} + 2 y z + 2 z x

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Solution

The correct option is B $2 x^{2} + 2 y^{2} + 4 x y + 2 y z + 2 z x$
$2 x (z + x + y) + 2 y (z + y + x)$
$= 2 z x + 2 x^{2} + 2 x y + 2 z y + 2 y^{2} + 2 y x$
$= 2 x^{2} + 2 y^{2} + 4 x y + 2 y z + 2 z x$
Hence, $B$ is correct.

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