question_answer

Find the product of\[\left( p\text{ }+\text{ }q\text{ }+\text{ }r \right)\text{ }[\text{ }{{\left( p\text{ }-\text{ }q \right)}^{2}}+{{\left( q\text{ }-\text{ }r \right)}^{2}}+\text{ }{{\left( r\text{ }-\text{ }p \right)}^{2}}]\].

A) \[{{p}^{3}}+{{q}^{3}}+{{r}^{3}}\]                      

B) \[{{p}^{3}}\text{ }+\text{ }{{q}^{3}}\text{ }+\text{ }{{r}^{3}}\text{ }\,3pqr\]

C) \[2\text{ }\left( {{p}^{3}}\text{ }+\text{ }{{q}^{3}}+{{r}^{3}}\text{ }-\text{ }3pqr \right)\]       

D) \[{{p}^{3}}\text{ }+\text{ }{{q}^{3}}+\,\,{{r}^{3}}+\,\,2\text{ }\left( pq\,\,+\,\,qr\,\,+\,\,rp \right)\]

E) None of these