(P-q)cube+ (q-rcube)+(r-p) cube
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using x³+y³+x³-3xyz=(x+y+z)(x²+y²+z²-xy-yz-zx)
If x + y + z = 0 ,
Then ,
x³ + y³ + z³ = 3xyz
Let x = p - q ,
y = q - r ,
z = r - p ;
Now ,
x + y + z = p - q + q - r + r - p
x + y + z = 0
Therefore ,
=x³ + y³ + z³ = 3xyz
=( p - q )³ + ( q - r )³ + ( r - p )³
= 3( p - q )( q - r )( r - p )
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