几道因式分解题～(1)x(m+n)^(m-n)-y(m+n)(n-m)^2(2)-6a^3(b-c)^2+3a(c-b)^3(3)-p(q+r-1)-q(r+q-1)+(1-q-r)(4)24xy^z^(x+y-z)-32xyz(z-x-y)^+8xyz^3(z-x-y)^=平方

Question

几道因式分解题～
(1)x(m+n)^(m-n)-y(m+n)(n-m)^2
(2)-6a^3(b-c)^2+3a(c-b)^3
(3)-p(q+r-1)-q(r+q-1)+(1-q-r)
(4)24xy^z^(x+y-z)-32xyz(z-x-y)^+8xyz^3(z-x-y)
^=平方

Answer 1

(1)x(m+n)^2(m-n)-y(m+n)(n-m)^2
=x(m+n)^2(m-n)-y(m+n)(m-n)^2
=(m+n)(m-n)[x(m+n)-y(m-n)]
=(m+n)(m-n)(xm+xn-ym+yn)
(2)-6a^3(b-c)^2+3a(c-b)^3
=-6a^3(b-c)^2-3a(b-c)^3
=-3a(b-c)^2[2a+(b-c)]
=-3a(b-c)^2(2a+b-c)
(3)-p(q+r-1)-q(r+q-1)+(1-q-r)
=-p(q+r-1)-q(q+r-1)-(q+r-1)
=-(q+r-1)(p+q+1)
=(1-q-r)(p+q+1)
(4)24xy^z^(x+y-z)-32xyz(z-x-y)^+8xyz^3(z-x-y)
=24xy^z^(x+y-z)+32xyz(x+y-z)^-8xyz^3(x+y-z)
=8xyz(x+y-z)[3yz+4(x+y-z)-z^2]
=8xyz(x+y-z)(3yz+4x+4y-4z-z^2)