分解因式:（1） (x-y)³-(x-y) （2）x³y³-2x²y²+xy

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

1x²y³－2x²y²＋xy =xy(xy²-2xy+1)

 2 a﹙x-y﹚-b﹙y－x﹚＋c﹙x－y﹚=a﹙x-y﹚+b﹙x-y﹚＋c﹙x－y﹚=(a+b+c)(x-y)

[﹙x－y﹚²＋﹙x＋y﹚﹙x－y﹚]÷2x,=(x^2-2xy+y^2+x^2-y^2)\2x=(2x^2-2xy)\2x=x-y=3-15=-12

(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

（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)(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