(xy-1)²+(x+y-2xy)(x+y-2)分解因式用换元法

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(xy-1)²+(x+y-2xy)(x+y-2)分解因式用换元法
(xy-1)²+(x+y-2xy)(x+y-2)分解因式用换元法

(xy-1)²+(x+y-2xy)(x+y-2)分解因式用换元法
令a=x+y-2xy
b=x+y-2
b-a=2xy-2=2(xy-1)
所以原式=[(b-a)/2]²+ab
=(b²-2ab+b²+4ab)/4
=(a²+2ab+b²)/4
=(a+b)²/4
=(2x+2y-2xy-2)²/4
=(xy-x-y+1)²
=(x-1)²(y-1)²

令x+y=a，xy=b
原式化为：
（b-1）^2+(a-2b)(a-2)
=b^2-2b+1+a^2-2a-2ab+4b
=b^2+2b+1+a^2-2a-2ab
=(a^2-2ab+b^2)+2(b-a)+1
=(b-a)^2+2(b-a)+1
=(b-a+1)^2
=(xy-x-y+1)^2
=(x-1)^2(y-1)^2

计算x²-x/x²×x/1-x和x²-4y²/x²+2xy+y²÷x+2y/x²+xy X²+xy²-x²-y²-3xy+2x+2y-1分解因式 x²-2xy+y²-9 (5x²y-2xy²-3xy)-(2xy+5x²y-2xy²),x=-1/5,y=-1/3 整式乘法..1.3xy（x²y-xy²+xy）-xy²（2x²-xy+2x）2.（x-1）（x²-4x+3）-x（x²-5x+2) 1 3x²+4xy-y²=2 4xy+1-4x²-y²= 若x²+xy-2y²=0,则x²+3xy+y²/x²+y² x²+xy-2y²=0则x²+3xy+y²/x²+y² 1.(8xy-x²+y²)-(x²-y²+8xy)2.(2x²-1/2+3x)-4(x-x²+1/2)3.3x²-[7x-(4x-3)-2x²] 1-x²+2xy-y²x²-y²+x-y麻烦用因式分解解 x²-4y²/x²+2xy+y²÷x+2y/2x²+2xy 已知xy=8满足x²y-xy²-x+y=56,求x²+y²x-3=y-2=z-1,求x²+y²+z²-xy-yz-zx因式分解如图 x³y³-x²y²-xy+1 因式分解 x²-XY-2y²-X-Y x²+xy-2y²-x+7y-6 因式分解2x(x-y)^4 - x²(x-y)² + xy(y-x)²RT 计算：4xy²-3x²y-{3x²y-[2xy²-4x²y+2(x²y-2xy²)]急（xy-x²）÷[（x²-2xy+y²）÷xy]*[(x-y)÷x²]