分解因式(x+y+z)³+(3x-2y-3z)³-(4x-y-2x)³两解,最好两解,

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/06 18:06:54
分解因式(x+y+z)³+(3x-2y-3z)³-(4x-y-2x)³两解,最好两解,

分解因式(x+y+z)³+(3x-2y-3z)³-(4x-y-2x)³两解,最好两解,
分解因式(x+y+z)³+(3x-2y-3z)³-(4x-y-2x)³
两解,最好两解,

分解因式(x+y+z)³+(3x-2y-3z)³-(4x-y-2x)³两解,最好两解,
(x+y+z)³+(3x-2y-3z)³-(4x-y-2z)³
=(x+y+z)³+[(3x-2y-3z)-(4x-y-2z)][(3x-2y-3z)²+(3x-2y-3z)(4x-y-2z)+(4x-y-2z)²]
=(x+y+z)³-(x+y+z)[(3x-2y-3z)²+(3x-2y-3z)(4x-y-2z)+(4x-y-2z)²]
=(x+y+z)[(x+y+z)²-(3x-2y-3z)²-(3x-2y-3z)(4x-y-2z)-(4x-y-2z)²]

设x+y+z=a,3x-2y-3z=b,那么4x-y-2z=a+b(题目肯定打错了)
a³+b³-(a+b)³
=a³+b³-(a³+b³+3a^2b+3ab^2)
=3ab(a+b)
=3(x+y+z)(3x-2y-3z)(4x-y-2z)没错,只要求分解因式我说错的是(4x-y-2x)...

全部展开

设x+y+z=a,3x-2y-3z=b,那么4x-y-2z=a+b(题目肯定打错了)
a³+b³-(a+b)³
=a³+b³-(a³+b³+3a^2b+3ab^2)
=3ab(a+b)
=3(x+y+z)(3x-2y-3z)(4x-y-2z)

收起