分式因解：x^n+1-8x^n+16x^n-1=（x+y)^2-4(x+y-1)(x+y)^m+1-(x+y)^m-1(m为大于1的正整数）x^2(y-x)+y^2(x-y)

Question

分式因解：x^n+1-8x^n+16x^n-1=
（x+y)^2-4(x+y-1)
(x+y)^m+1-(x+y)^m-1(m为大于1的正整数）
x^2(y-x)+y^2(x-y)

Answer 1

x^n+1-8x^n+16x^n-1=x^(n-1)(x²-8x+16)
=x^(n-1)*(x-4)²
（x+y)^2-4(x+y-1)
=( x+y)²-4(x+y)+4
=(x+y-2)²
(x+y)^m+1-(x+y)^m-1(m为大于1的正整数）
=(x+y)^(m-1)(x+y+1)(x+y-1)
x^2(y-x)+y^2(x-y)
=x²(y-x)-y²(y-x)
=(y-x)(x²-y²）
=-(x+y)(x-y)²