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f(x,y)=3(x+y)+32xy f(x,y)=3(x+y)-32xy f(x,y)=3(x+y)-16xy f(x,y)=3(x+y)+16xy
2x2y3+y+3xy 2x2y2﹣2y+3xy 2x2y3+2y﹣3xy 2x2y3+y﹣3xy
f(x,y)=3(x+y)-32xy f(x,y)=3(x+y)-16xy f(x,y)=3(x+y)+32xy f(x,y)=3(x+y)+16xy
f(x,y)=3(x+y)+32xy f(x,y)=3(x+y)-32xy f(x,y)=3(x+y)-16xy f(x,y)=3(x+y)+16xy
若X→Y,Y→Z,则X→Z 若X→Y,X→Z,则X→YZ 若X→Z,则XY→Z 若XY→Z,则X→Z,Y→Z
xy(2x-2y)2 2xy(x-y)2 4xy(x2-2xy+y2) 4xy(x-y)2
f(xy)=f(x)f(y) f(xy)=f(x)+f(y) f(x+y)=f(x)f(y) f(x+y)=f(x)+f(y)
f(x,y)=3(x+y)+32xy f(x,y)=3(x+y)-32xy f(x,y)=3(x+y)-16xy f(x,y)=3(x+y)+16xy
exy[xsin(x+y)-cos(x+y)] exy[xsin(x+y)+cos(x+y)] exy[xsinxy+cos(x+y)] exy[ysin(x+y)+xcos(x+y)]
f(x,y)=3(x+y)+32xy f(x,y)=3(x+y)-32xy f(x,y)=3(x+y)-16xy f(x,y)=3(x+y)+16xy
x2 –2xy+y2=x(x-2y)+y2 x2-16y2=(x+8y)(x-8y)
x2+xy+y2=(x+y)2 x4y4-1=(x2y2+1)(xy+1)(xy-1)
D(XY)=D(X)D(Y) D(X+Y)=D(X)+D(Y) X和Y独立 X和Y不独立
exy[xsin(x+y)-cos(x+y)] exy[xsin(x+y)+cos(x+y)] exy[xsinxy+cos(x+y)] exy[ysin(x+y)+xcos(x+y)]
f(x,y)=3(x+y)+32xy f(x,y)=3(x+y)-32xy f(x,y)=3(x+y)-16xy f(x,y)=3(x+y)+16xy
f(x,y)=3(x+y)+32xy f(x,y)=3(x+y)-32xy f(x,y)=3(x+y)-16xy f(x,y)=3(x+y)+16xy
若X→Y,WY→Z,则XW→Z 若X→Y,Y→Z,则XY→Z 若XY→Z,则X→Z,Y→Z 若X→Y,则Y→Z,则X→Z
exy[xsin(x+y)-cos(x+y)] exy[xsin(x+y)+cos(x+y)] exy[xsinxy+cos(x+y)] exy[ysin(x+y)+xcos(x+y)]
2x2-xy-x=2x(x-y-1) -xy2+2xy-3y=-y(xy-2x-3) x(x-y)-y(x-y)=(x-y)2 x2-x-3=x(x-1)-3
-x2-y2 = -(x+y)(x-y) x2y+2xy+4y = y(x+2)2 -49x2+x2y2 = (xy+7x)(xy-7x) 16x2+4y2-16xy = 4(2x-y)2