Question:
Find the value
$\frac{1}{27} x^{3}-y^{3}+125 z^{3}+5 x y z$
Solution:
$=(x / 3)^{3}+(-y)^{3}+(5 z)^{3}-3 \times x / 3(-y)(5 z)$
$=(x / 3+(-y)+5 z)\left((x / 3)^{2}+(-y)^{2}+(5 z)^{2}-x / 3(-y)-(-y) 5 z-5 z(x / 3)\right)$
$=(x / 3-y+5 z)\left(x^{2} / 9+y^{2}+25 z^{2}+x y / 3+5 y z-5 z x / 3\right)$
$\therefore \frac{1}{27} \mathrm{x}^{3}-\mathrm{y}^{3}+125 \mathrm{z}^{3}+5 \mathrm{xyz}$
$=(x / 3-y+5 z)\left(x^{2} / 9+y^{2}+25 z^{2}+x y / 3+5 y z-5 z x / 3\right)$