分解因式:（1） (x-y)³-(x-y) （2）x³y³-2x²y²+xy （3）a³c-4a²bc+4ab²c （4）（x²+y²）²-4x²y²

分解因式:（1） (x-y)³-(x-y) （2）x³y³-2x²y²+xy （3）a³c-4a²bc+4ab²c （4）（x²+y²）²-4x²y²
分解因式:（1） (x-y)³-(x-y) （2）x³y³-2x²y²+xy （3）a³c-4a²bc+4ab²c （4）（x²+y²）²-4x²y²

分解因式:（1） (x-y)³-(x-y) （2）x³y³-2x²y²+xy （3）a³c-4a²bc+4ab²c （4）（x²+y²）²-4x²y²
（1） (x-y)³-(x-y)
＝(x-y)[(x-y)²-1]
=(x-y)(x-y+1)(x-y-1)
（2）x³y³-2x²y²+xy
=xy(x²y²-2xy+1)
=xy(xy-1)²
（3）a³c-4a²bc+4ab²c
=ac(a²-4ab+4b²)
=ac(a-2b)²
（4）（x²+y²）²-4x²y²
=(x²+y²+2xy)(x²+y²-2xy)
=(x+y)²(x-y)²

(x-y)³-(x-y)
=(x-y) {(x-y)²-1}
=(x-y)(x-y-1)(x-y+1）
x³y³-2x²y²+xy
=xy(x²y²-2xy+1)
=xy(xy-1)²
a³c-4a²bc+4ab²c
=a...

全部展开

(x-y)³-(x-y)
=(x-y) {(x-y)²-1}
=(x-y)(x-y-1)(x-y+1）
x³y³-2x²y²+xy
=xy(x²y²-2xy+1)
=xy(xy-1)²
a³c-4a²bc+4ab²c
=ac(a²-4ab+4b²)
=ac(a-2b)²
（x²+y²）²-4x²y²
=x^4+2x²y²+y^4-4x²y²
=x^4-2x²y²+y^4
=(x²-y²)²
=(x+y)²(x-y)²

收起

(x-y)³-(x-y)=(x-y)(x²+y²-2xy-1)
x³y³-2x²y²+xy =xy(x²y²-2xy+1)=xy(xy-1)²
a³c-4a²bc+4ab²c=ac(a²-4ab+4b²)=ac(a-4b)²
(x²+y²）²-4x²y² =(x²+y²+2xy)(x²-2xy+y²)=(x+y)²(x-y)²