Expand the following: $(x + 2 y + 4 z)^{2}$

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Solution

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

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