गुणनखण्ड कीजिए:
`p^(3)(q-r)^(3)+q^(3)(r-p)^(3)+r^(3)(p-q)^(3)`

Explanation

दिया है,
`p^(3)(q-r)^(3)+q^(3)(r-p)^(3)+r^(3)(p-q)^(3)={p(q-r)}^(3)+{q(r-p)}^(3)+{r(p-q)}^(3)`
माना `p(q-r)=a,q(r-p)=b` तथा r(p-q)=c तो,
`a+b+c=p(q-r)+q(r-p)+r(p-q)`
`=pq-pr+qr-qp+rp-rq=pq-pr+qr-pq+pr-qr=0`
`thereforea^(3)+b^(3)+c^(3)=3abc`
`implies{p(q-r)}^(3)+{q(r-p)}^(3)+{r(p-q)}^(3)=3p(q-r)xxq(r-p)xxr(p-q)`
`impliesp^(3)(q-r)^(3)+q^(3)(r-p)^(3)+r^(3)(p-q)^(3)=3pqr(p-q)(q-r)(r-p)`