Factorise :
p^3(q-r) + q^3(r-p) + r^3(p-q) ?
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Answer:
We know the corollary: if a+b+c=0 then a
3
+b
3
+c
3
=3abc
Using the above corollary taking a=p(q−r), b=q(r−p) and c=r(p−q), we have a+b+c=p(q−r)+q(r−p)+r(p−q)=pq−pr+qr−pq+pr−qr=0 then the equation p
3
(q−r)
3
+q
3
(r−p)
3
+r
3
(p−q)
3
can be factorised as follows:
p
3
(q−r)
3
+q
3
(r−p)
3
+r
3
(p−q)
3
=3[p(q−r)×q(r−p)×r(p−q)]=3pqr(q−r)(r−p)(p−q)
Hence, p
3
(q−r)
3
+q
3
(r−p)
3
+r
3
(p−q)
3
=3pqr(q−r)(r−p)(p−q)
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