Question:
Find the value
$(2 x-3 y)^{3}+(4 z-2 x)^{3}+(3 y-4 z)^{3}$
Solution:
Let $2 x-3 y=a, 4 z-2 x=b, 3 y-4 z=c$
$\therefore a+b+c=2 x-3 y+4 z-2 x+3 y-4 z=0$
$\because a+b+c=0 \therefore a^{3}+b^{3}+c^{3}=3 a b c$
$=3(2 x-3 y)(4 z-2 x)(3 y-4 z)$
$\therefore(2 x-3 y)^{3}+(4 z-2 x)^{3}+(3 y-4 z)^{3}$
$=3(2 x-3 y)(4 z-2 x)(3 y-4 z)$
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