Factorise: (3 a-2 b)^3+(2 b-5 c)^3+(5 c-3 a)^3 - Vidyadip

Question

Factorise:
$(3 a-2 b)^3+(2 b-5 c)^3+(5 c-3 a)^3$

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Answer

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,
$(3 a-2 b)^3+(2 b-5 c)^3+(5 c-3 a)^3=x^3+y^3+z^3$
$=3 x y z\left[\text { Here, } x+y+z=0 . \text { So, } x^3+y^3+z^3\right]$
$=(3 a-2 b)(2 b-5 c)(5 c-3 a)$

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