(x+2y+3z)2=

${(x + 2 y + 3 z)}^{2} =$

A
$x^{2} - 4 y^{2} + 9 z^{2} + 4 x y - 12 y z - 6 z x$
B
$x^{2} + 4 y^{2} + 9 z^{2} + 4 x y + 12 y z + 6 z x$
C
$x^{2} - 4 y^{2} - 9 z^{2} + 4 x y + 12 y z - 6 z x$
D
$x^{2} - 4 y^{2} + 9 z^{2} + 4 x y + 12 y z - 6 z x$

Solution:

{(x + 2 y + 3 z)}^{2}

${(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$

$= x^{2} + {(2 y)}^{2} + {(3 z)}^{2} + 2. x .2 y + 2.2 y .3 z + 2.3 z . x$

$= x^{2} + 4 y^{2} + 9 z^{2} + 4 x y + 12 y z + 6 z x$

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