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Factorise (p-q)^3+(q-r)^3+(r-p)^3....

Factorise `(p-q)^3+(q-r)^3+(r-p)^3`.

Text Solution

Verified by Experts

Putting `(p-q)=x,(q-r)=y and (r-p)=z`, we get
`(p-q)^3+(q-r)^3+(r-p)^3`
`=x^3+y^3+z^3, " where " (x+y+z)=(p-q)+(q-r)+(r-p)=0`
`=3xyz " "[because x+y+z=0 rArr x^3+y^3+z^3=3xyz]`
`=3(p-q)(q-r)(r-p)`.
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