Question

帮忙把下列各式分解因式

(1): (x-m)^3(x-n)+(x-m)^2(n-m)^2(n-x)
(2): -a(b-a)^2-ab(a-b)^2+ac(b-a)^2
(3): a^2(b-a)^4-ab(a-b)^4-ac(a-b)^5
(4): (x+y)^n+2 - (x-y)^n+1 +(x+y)^n

Answer 1

(1): (x-m)^3(x-n)-(x-m)^2(n-m)^2(x-n)
[(x-m)^2(x-n)][x-m-(n-m)^2]
(2): -a(b-a)^2-ab(a-b)^2+ac(b-a)^2
=a(c+b-a)(b-a)2
(3): a^2(b-a)^4-ab(a-b)^4-ac(a-b)^5
= a^2(b-a)^4-ab(b-a)^4+ac(b-a)^5
= a(b-a)^4[a-b+c(b-a)]
(4): (x+y)^n+2 - (x-y)^n+1 +(x+y)^n
=(x+y)^n[(x+y)^2-(x-y)+1]

Answer 2

(x-m)^3(x-n)+(x-m)^2(n-m)^2(n-x)
=﹙x-n﹚﹙x-m﹚�0�5[x-m-﹙n-m﹚�0�5]
=﹙x-n﹚﹙x-m﹚�0�5﹙x-m-n�0�5-m�0�5+2mn﹚
-a(b-a)^2-ab(a-b)^2+ac(b-a)^2
=a﹙a-b﹚�0�5﹙c－b－1﹚