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