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Find the value

Question:

Find the value

$8 x^{3}+27 y^{3}-216 z^{3}+108 x y z$

Solution:

$=(2 x)^{3}+(3 y)^{3}+(-6 y)^{3}-3(2 x)(3 y)(-6 z)$

$=(2 x+3 y+(-6 z))\left((2 x)^{2}+(3 y)^{2}+(-6 z)^{2}-2 x+3 y-3 y(-6 z)-(-6 z) 2 x\right)$

$=(2 x+3 y+(-6 z))\left(4 x^{2}+9 y^{2}+36 z^{2}-6 x y+18 y z+12 z x\right)$

$? 8 x^{3}+27 y^{3}-216 z^{3}+108 x y z$

$=(2 x+3 y+(-6 z))\left(4 x^{2}+9 y^{2}+36 z^{2}-6 x y+18 y z+12 z x\right)$

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