1) (x+y)^2-(x+y)^3 2) (x-y)^2-(x-y)^3 3)(x-y)^2-(y-x)^3 因式分解
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1) (x+y)^2-(x+y)^3 2) (x-y)^2-(x-y)^3 3)(x-y)^2-(y-x)^3 因式分解
因式分解 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)^2-6a^2b(a+b) 6) (x+y)^2(x-y)+(x+y)(x-y)^2 7) 2a(a-3)^2-6a^2(3-a)+8a(a-3)
8) 24xy^2z^2(x+y-z)-32xyz(z-x-y)^2+8xyz^3(z-x-y)
因式分解 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)^2-6a^2b(a+b) 6) (x+y)^2(x-y)+(x+y)(x-y)^2 7) 2a(a-3)^2-6a^2(3-a)+8a(a-3)
8) 24xy^2z^2(x+y-z)-32xyz(z-x-y)^2+8xyz^3(z-x-y)
1) (x+y)^2-(x+y)^3 =(x+y)²[1-(x+y)]=(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)^2-6a^2b(a+b) =2ab(a+b)(2a+2b-3a)=-2ab(a+b)(a-2b)
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)^2-6a^2(3-a)+8a(a-3)=2a(a-3)²+6a²(a-3)+8a(a-3)
=2a(a-3)(a-3a+4)=-4a(a-3)(a-2)
8) 24xy^2z^2(x+y-z)-32xyz(z-x-y)^2+8xyz^3(z-x-y)
=24xy²z²(x+y-z)-32xyz(x+y-z)²-8xyz³(x+y-z)
=8xyz(x+y-z)[3yz-4(x+y-z)-z²]
=8xyz(3yz-4x-4y+4z-z²)
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)^2-6a^2b(a+b) =2ab(a+b)(2a+2b-3a)=-2ab(a+b)(a-2b)
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)^2-6a^2(3-a)+8a(a-3)=2a(a-3)²+6a²(a-3)+8a(a-3)
=2a(a-3)(a-3a+4)=-4a(a-3)(a-2)
8) 24xy^2z^2(x+y-z)-32xyz(z-x-y)^2+8xyz^3(z-x-y)
=24xy²z²(x+y-z)-32xyz(x+y-z)²-8xyz³(x+y-z)
=8xyz(x+y-z)[3yz-4(x+y-z)-z²]
=8xyz(3yz-4x-4y+4z-z²)
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