Question

在线等几道分解因式计算题。要过程

p (1-p)3 (1+p)3 - p2 (p-1)2 (1+p)3 ；

x (x-y)2 + x (x+y) (y-x) +2 (x-y) ；

a (a-b-c) + b (b+c-a) + c (c-a+b)

Answer 1

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

Answer 2

p (1-p)3 (1+p)3 - p2 (p-1)2 (1+p)3 =p(1+p)^3(1-p)^2(1-p-p)=(1-2p)p(1+p)^3(1-p)^2

x (x-y)2 + x (x+y) (y-x) +2 (x-y) =(x-y)[x^2-xy-x^2-xy+2]=2(1-xy)(x-y)

a (a-b-c) + b (b+c-a) + c (c-a+b)=a^2-ab-ac+b^2+bc-ab+c^2-ac+bc=a^2-2ab-2ac+b^2+2bc+c^2
=a^2-2a(b+c)+(b+c)^2=(a-b-c)^2

Answer 3

（2）原式=x(x-y)(x-y+x+y+2)=x(x-y)(2x+2)=2x(x-y)(x+1)