Question

Factorize:
(3a − 2b)³ + (2b − 5c)³ + (5c − 3a)³

Answer 1

Put $3a-2b=x,2b-5c=y$ and$5c-3a=z.$

We have:

$x+y+z=3a-2b+2b-5c+5c-3a=0$

Now,

$(3a-2b{)}^3+(2b-5c{)}^3+(5c-3a{)}^3$

$=x^3+y^3+z^3$

$=3xyz$

Here, $x+y+z=0.$

So,$x^3+y^3+z^3=3xyz$

$=3\left[\right(a-2b)\times (2b-5c)\times (5c-3a\left)\right]$