三次方的因式分解,要详细的过程x³-3x²+4=ab(c²-d²)+cd(a²-b²)=x²-4mx+8mn-4n⁴=x⁴+64=x³-11x²+31x-21=x³-4xy²-2x²y+8y³=

1、
原式=x^3+1-3(x^2-1)
=(x+1)(x^2-x+1)-3(x+1)(x-1)
=(x+1)(x^2-x+1-3x+3)
=(x+1)(x^2-4x+4)
=(x+1)(x-2)^2
2、
原式=abc^2-abd^2+a^2cd-b^2cd
=(abc^2+a^2cd)-(abd^2+b^2cd)
=ac*(bc+ad)-bd*(ad+bc)
=(ac-bd)(ad+bc)
3、
x^2-4mx+8mn-4n^2【这里应该是平方】
=(x^2-4mx+4m^2)-4m^2+8mn-4n^2
=(x-2m)^2-(4m^2-8mn+4n^2)
=(x-2m)^2-(2m-2n)^2
=(x-2m+2m-2n)*(x-2m-2m+2n)
=(x-2n)*(x-4m+2n)
4、
x^4+64
=x^4+16x^2+64-16x^2
=(x^2+8)^2-(4x)^2
=(x^2+4x+8)(x^2-4x+8)
5、
原式=(x^3-1)-11x^2+31x-20
=(x^3-1)-(11x^2-31x+20)
=(x-1)(x^2+x+1)-(11x-20)(x-1)
=(x-1)(x^2+x+1-11x+20)
=(x-1)(x^2-10x+21)
=(x-1)(x-3)(x-7)
6、
原式=x*(x^2-4y^2)-2y*(x^2-4y^2)
=(x-2y)(x^2-4y^2)
=(x-2y)(x+2y)(x-2y)
=(x+2y)(x-2y)^2

x³-3x²+4=(x³+x²)-4（x²-1）=x²（x+1）-4（x+1)(x-1)=(x+1)(x²-4x+4)=(x+1）（x-2)²
ab(c²-d²)+cd(a²-b²)=abc²-abd²+cda²-cdb²=abc²+cda²-(abd²+cdb²)=ac(bc+ad)-bd(ad+bc)=(ad+bc)(ac-bd)
x²-4mx+8mn-4n⁴=
x⁴+64=
x³-11x²+31x-21=
x³-4xy²-2x²y+8y³=

1、原式=（x³-x²)-(4x²-4)=x²(x-1)-4(x+1)(x-1)=(x-1)(x²-4x-4)
2、原式=abc²-abd²+a²cd-b²cd=(abc²+a²cd)-(abd²+b²cd)=ac(bc+ad)-bd(ad+bc)=(ad+bc)(ac-bd)
3、原式=（x²-4mx+4m²)-(4m²-8mn+4n²)=(x-2m)²-(2m-2n)²
=(x-2m+2m-2n)(x-2m-2m+2n)=(x-2n)(x-4m+2n)--------题目有错,该是：-4n²
4、原式=（x²+8)²-16x²=(x²+4x+8)(x²-4x+8)
5、原式=（x³-x²)-(10x²-10x)+(21x-21)=x²(x-1)-10x(x-1)+21(x-1)=(x-1)(x²-10x+21)=(x-1)(x-3)(x-7)
6、原式=（x³-2x²y)-(4xy²-8y³)=x²(x-2y)-4y²(x-2y)=(x-2y)(x²-4y²)=(x-2y)(x+y)(x-y)