p (1-p)^3 (1+p)^3 - p^2 (p-1)^2 (1+p)^3 ；
=p[ (1-p) (1+p)]^3 - p^2 (p-1)^2 (1+p)^2(1+p)
=p[ (1-p^2)]^3 - p^2 [(p-1) (1+p)]^2(1+p)
=p(1-p^2)^3 - p^2 (p^2-1)^2(1+p)
=p(1-p^2)^3 -p^2 (1-p^2)^2(1+p)
=p(1-p^2)^2(1-p^2) -p^2 (1-p^2)^2(1+p)
=p(1-p^2)^2[(1-p^2) -p (1+p)]
=p(1-p^2)^2(1-p^2 -p-p^2)
=p(1-p^2)^2(1-p-2p^2)
=p[(1-p)(1+p)]^2(1-2p)(1+p)
=p(1-p)^2(1+p)^2(1-2p)(1+p)
=p(1-2p)(1-p)^2(1+p)^3
x (x-y)^2 + x (x+y) (y-x) +2 (x-y) ；
=x (x-y)^2 -x (x+y) (x-y) +2 (x-y)
= (x-y) [x (x-y) -x (x+y) +2]
= (x-y) (x^2-xy -x^2-xy +2)
= (x-y) (2-2xy)
=2 (x-y) (1-xy)
a(a-b-c)+b(b+c-a)+c(c-a+b)
=a(a-b-c)+b(-a+b+c)+c(-a+b+c)
=a(a-b-c)-b(a-b-c)-c(a-b-c)
=(a-b-c)(a-b-c)
=(a-b-c)^2