Question

分解因式:(1)(x+y)²-(x+y)³

（2）(x-y)²-(x-y)³(3) (x-y)²-(y-x)³(4)2(x-y)-3(y-x)²(5)4ab(a+b)²-6a²b(a+b) (6)(x+y)²(x-y)+(x+y)(x-y)²(7)2a(a-3)²-6a²(3-a)+8a(a-3) (8)24xy²z²(x+y-z)-32xyz(z-x-y)²+8xyz³(z-x-y)好的我给20分！
(3) (x-y)²-(y-x)³
(4)2(x-y)-3(y-x)²
(5)4ab(a+b)²-6a²b(a+b)

Answer 1

分解因式:
(1)(x+y)²-(x+y)³
=(x+y)^2*(1-x-y)
（2）(x-y)²-(x-y)³
=(x-y)^2(1-x+y)
(3) (x-y)²-(y-x)³
=(y-x)^2-(y-x)^3
=(y-x)^2(1-y+x)
(4)2(x-y)-3(y-x)²
=(x-y)[2-3(x-y)]
(5)4ab(a+b)²-6a²b(a+b)
=4ab*(a+b)[(a+b)-1.5a]
=4ab*(a+b)(b-0.5b)
(6)(x+y)²(x-y)+(x+y)(x-y)²
=(x+y)(x-y)[(x+y)+(x-y)]
=2x(x+y)(x-y) .
(7)2a(a-3)²-6a²(3-a)+8a(a-3)
=2a(a-3)[(a-3)+3a+4]
=2a(a-3)(4a+1)
(8)24xy²z²(x+y-z)-32xyz(z-x-y)²+8xyz³(z-x-y)
=8xyz*(x+y-z)[3yz+4-1]
=8xyz(x+y-z)(3yz+3) .

Answer 2

（2）(x-y)²-(x-y)³=(x-y)²(1-x+y)

Answer 3

:(1)(x+y)²-(x+y)³
=(x+y)²(1-x-y)

（2）(x-y)²-(x-y)³
=(x-y)²(1-x+y)

(3) (x-y)²-(y-x)³
=(y-x)²(1-y+x)

(4)2(x-y)-3(y-x)²
=2(x-y)-3(x-y)²
=(x-y)(2-3x+3y)

(5)4ab(a+b)²-6a²b(a+b)
=2ab(2a+2b-3a)
=2ab(2b-a)

(6)(x+y)²(x-y)+(x+y)(x-y)²
=(x+y)(x-y)(x+y+x-y)
=2x(x+y)(x-y)

(7)2a(a-3)²-6a²(3-a)+8a(a-3)
=2a(a-3)(a-3+2a+4)
=2a(a-3)(3a+1)

(8)24xy²z²(x+y-z)-32xyz(z-x-y)²+8xyz³(z-x-y)
=8xyz(x+y-z)(3yz-4z-4x-4y-2z²)

Answer 4

:(1)(x+y)²-(x+y)³
=(x+y)²(1-x-y)

（2）(x-y)²-(x-y)³
=(x-y)²(1-x+y)

(3) (x-y)²-(y-x)³
=(x-y)²+(x-y)³
=(x-y)²(1+x-y)

(4)2(x-y)-3(y-x)²
=2(x-y)-3(x-y)²
=(x-y)(2-3x+3y)

(5)4ab(a+b)²-6a²b(a+b)
=2ab(a+b)(2a+2b-3a)
=2ab(a+b)(2b-a)

(6)(x+y)²(x-y)+(x+y)(x-y)²
=(x+y)(x-y)(x+y+x-y)
=2x(x+y)(x-y)

(7)2a(a-3)²-6a²(3-a)+8a(a-3)
=2a(a-3)²+6a²(a-3)+8a(a-3)
=2a(a-3)(a²-6a+9+3a+4)
=2a(a-3)(a²-3a+13)

(8)24xy²z²(x+y-z)-32xyz(z-x-y)²+8xyz³(z-x-y)
=24xy²z²(x+y-z)+32xyz(x+y-z)²-8xyz³(x+y-z)
=8xyz(x+y-z)(3yz+4-z²)

Answer 5

有点难度