Question

factorise:
p^3(q-r)^3 + q^3(r-p)^3 + r^3(p-q)^3​

Answer 1

=>p^3(q-r)^3 + q^3(r-p)^3 + r^3(p-q)^3

=>p^3(q^3 - r^3 - 3rq^2 + 3qr^2) + q^3(r^3

- p^3 - 3pr^2 + 3rp^2) + r^3(p^3 - q^3 -

3qp^2 + 3pq^2)

=>(pq)^3 - (pr)^3 -3pqr(qp^2) + 3pqr(rp^2)

+ (qr) ^3-(pq)^3 - 3pqr(rq^2) + 3pqr(pq^2) + (pr)^3 - (qr)^3 -3pqr(pr^2) + 3pqr(qr^2)

=>-3pqr(qp^2) + 3pqr(rp^2) - 3pqr(rq^2) +

3pqr(pq^2) - 3pqr(pr^2) + 3pqr(qr^2)

=>3pqr(pq^2+qr^2+rp^2)

-3pqr(qp^2+rq^2+pr^2)

=>3pqr[(pq^2+qr^2+rp^2)

- (qp^2+rq^2+pr^2)]

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