Question

p(q^2-r^2)+q(r^2-p^2)+r(p^2-q^2)如何因式分解

Answer 1

p(q^2-r^2)+q(r^2-p^2)+r(p^2-q^2)

=p*q^2-p*r^2+q*r^2-q*p^2+r*p^2-r*q^2

=(p*q^2-q*p^2)-(p*r^2-q*r^2)+(r*p^2-r*q^2)

=(p-q)[-pq-r^2+r(p+q)]

=(p-q)(-pq-r^2+rp+rq)

=(p-q)(-pq+rp+rq-r^2)

=(p-q)(q-r))(r-p)