Question

这里有几到较难的因式分解题想请教一下

Answer 1

1、x^4+1993x^2+1992x+1993=
x^4-x+1993x^2+1993x+1993
=x(x-1)(x^2+x+1)+1993(x^2+x+1)
=(x^2+x+1)(x^2-x+1993)
2、=x(y+z)^2+y(z+x)^2+z(x+y)^2-4xyz
=x(y^2+2yz+z^2)+y(z^2+2xz+x^2)+z(x^2+2xy+y^2)-4xy
=xy^2+xz^2+yz^2+yx^2+zx^2+zy^2+6xyz-4xyz
=xy^2+xz^2+yz^2+yx^2+zx^2+zy^2+2xyz
=yx^2+zx^2+xy^2+xz^2+2xyz+yz^2+zy^2
=(y+z)x^2+(y^2+2yz+z^2)x+yz(y+z)
=(y+z)x^2+(y+z)^2x+yz(y+z)
=(y+z)[x^2+x(y+z)+yz]
=(y+z)(x+y)(x+z)
http://zhidao.baidu.com/question/199466092.html
3、a^5+a+1=
a^5-a^2+a^2+a+1=a^2(a^3-1)+(a^2+a+1)=a^2(a-1)(a^2+a+1)+(a^2+a+1)
=(a^2+a+1)(a^3-a^2+1)
4、(a+b+c)((bc+ca+ab)-abc
=（a+b)(b+c)(c+a)

5、(ax-by)^3+(by-cz)^3-(ax-cz)^3
=(ax-by+by-cz)[(ax-by)^2-(ax-by)(by-cz)+(by-cz)^2]-(ax-cz)^3
=(ax-cz)[(ax-by)^2-(ax-by)(by-cz)+(by-cz)^2-(ax-cz)^2]