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Question

The factors of (p−q)3+(q−r)3+(r−p)3 are:


A

pq(r+p)+qr(p+q)

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B

3(p-q)(q-r)(r-p)

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C

3(pq)(qr)(rp)

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D

3(p+q)(q+r)(r+p)

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Solution

The correct option is B

3(p-q)(q-r)(r-p)


Let a=pq,b=qr and c=rp
We see that
a+b+c=(pq)+(qr)+(rp)=0
Now, we know that a3+b3+c33abc=(a+b+c)(a2+b2+c2abbcca)
if (a+b+c)=0 then a3+b3+c33abc=0
a3+b3+c3=3abc
(pq)3+(qr)3+(rp)3
=3(pq)(qr)(rp)


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