Question:
Factorize:
$(3 a-2 b)^{3}+(2 b-5 c)^{3}+(5 c-3 a)^{3}$
Solution:
Put $(3 a-2 b)=x,(2 b-5 c)=y$ and $(5 c-3 a)=z$.
We have :
$x+y+z=3 a-2 b+2 b-5 c+5 c-3 a=0$
Now,
$(3 a-2 b)^{3}+(2 b-5 c)^{3}+(5 c-3 a)^{3}=x^{3}+y^{3}+z^{3}$
$=3 x y z \quad\left[\right.$ Here,$x+y+z=0 .$ So, $\left.x^{3}+y^{3}+z^{3}=3 x y z\right]$
$=3(3 a-2 b)(2 b-5 c)(5 c-3 a)$
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