因式分解:a(x-y)的n次方-3b(y-x)的n+1次方+2c(y-x)的n+2次方(n为正整数)

分两种情况：
1.n为奇数时
a(x-y)的n次方-3b(y-x)的n+1次方+2c(y-x)的n+2
=a(x-y)^n－3b(x－y)^(n＋1)－2c(x－y)^(n＋2)
=(x-y)^n*[a－3b(x－y)－2c(x－y)²]
=(x-y)^n*(a－3bx＋3by－2cx²＋4cxy－2cy²)
2.当n为偶数时
a(x-y)的n次方-3b(y-x)的n+1次方+2c(y-x)的n+2
=a(x-y)^n＋3b(x－y)^(n＋1)＋2c(x－y)^(n＋2)
=(x-y)^n[a＋3b(x－y)＋2c(x－y)²]
=(x-y)^n(a＋3bx－3by＋2cx²－4cxy＋2cy²)