因试分解

以下是整系数范围内分解：

(1)-2x^(5n-1)y^n+4x^(3n-1)y^(n+2)-2x^(n-1)y(n+4)
=-2x^(n-1)y^n*(x^4n-2x^2n*y^2+y^4)
=-2x^(n-1)y^n*(x^2n-y^2)^2

(2)x^3-8y^3-z^3-6xyz
=x^3-3*x^2*z+3*x*z^2-z^3-8y^3+3*x^2*z-3*x*z^2-6xyz
=(x-z)^3-(2y)^3+3xz(x-2y-z)
=(x-z-2y)((x-z)^2+(x-z)*2y+(2y)^2)+3xz(x-2y-z)
=(x-2y-z)(x^2+4y^2+z^2+2xy+xz-2yz)

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

(4)a^7-a^5*b^2+a^2*b^5-b^7
=a^5(a^2-b^2)+b^5(a^2-b^2)
=(a^5+b^5)(a^2-b^2)
=(a+b)(a^4+a^3*b+a^2*b^2+a*b^3+b^4)(a+b)(a-b)
=(a+b)^2*(a-b)*(a^4+a^3*b+a^2*b^2+a*b^3+b^4)

(5)x^3-9x+8
=x^3-1-9x+9
=(x-1)(x^2+x+1)-9(x-1)
=(x-1)(x^2+x-8)

(6)x^9+x^6+x^3-3
=(x^9-1)+(x^6-1)+(x^3-1)
=(x-1)(x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)+(x-1)(x^5+x^4+x^3+x^2+x+1)+(x-1)(x^2+x+1)
=(x-1)(x^8+x^7+x^6+2x^5+2x^4+2x^3+3x^2+3x+3)

好累……