Question

(P-q)cube+ (q-rcube)+(r-p) cube

Answer 1

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 )