Ta có :

  A=xy(x+y+z) -xyz +(yz+zx)(x+y+z) 
A=xy(x+y+z -z) + z(x+y)(x+y+z) 
A=xy(x+y) +z(x+y)(x+y+z) 
A=(x+y)(xy+z(x+y+z)) 
A=(x+y)(xy+zx+z(y+z)) 
A=(x+y)(x(y+z)+z(y+z)) 
A=(x+y)(y+z)(x+z)

P/ s : ko biết có đúng ko

Ta có 

A=(x+y)(xy+yz+xz)+z(xy+yz+xz)-xyz

  =(x+y)(xy+yz+xz)+xyz+z^2(y+x)-xyz

  = (x+y)(xy+yz+xz + z^2)

  = (x+y)(y+z)(x+z)

k cho mk đi

(xy+yz+zx)(x+y+z)-xyz

= (xy+yz)(x+y+z)+ x²z+xyz+ xz²-xyz

= (xy+yz)(x+y+z)+ x²z + xz²

= (x+z)(xy+y²+zy)+ xz(x+z) = (x+z)(xy+y²+zy+xz) = (x+z)(x+y)(x+z) 

A=x²y+xy²+xyz+xyz+y²z+yz²+x²z+xyz+xz²-xyz

A=(x²y+xy²+xyz+y²z)+(yz²+x²z+xyz+xz²)

A=y(x²+xy+xz+yz)+z(yz+x²+xy+xz)

A=(y+z)(x²+xy+xz+yz)

A=(y+z)[x(x+y)+z(x+y)]

A=(y+z)(x+y)(x+z)

xy(x+y+z) -xyz +(yz+zx)(x+y+z) 
=xy(x+y+z -z) + z(x+y)(x+y+z) 
=xy(x+y) +z(x+y)(x+y+z) 
=(x+y)(xy+z(x+y+z)) 
=(x+y)(xy+zx+z(y+z)) 
=(x+y)(x(y+z)+z(y+z)) 
=(x+y)(y+z)(x+z)

Ta có

C = xyz – (xy + yz + zx) + x + y + z – 1

= (xyz – xy) – (yz – y) – (zx – x) + (z – 1)

= xy(z – 1) – y(z – 1) – x(z – 1) + (z – 1)

= (z – 1)(xy – y – x + 1)

= (z – 1).[y(x – 1) – (x – 1)]

= (z – 1)(y – 1)(x – 1)

Với x = 9; y = 10; z = 101 ta có

C = (101 – 1)(10 – 1)(9 – 1) = 100.9.8 = 7200

Đáp án cần chọn là: C

\(=\dfrac{xy\left(z-1\right)-y\left(z-1\right)-x\left(z-1\right)+\left(z-1\right)}{xy\left(z+1\right)+y\left(z+1\right)-x\left(z+1\right)-\left(z+1\right)}\\ =\dfrac{\left(z-1\right)\left(xy-y-x+1\right)}{\left(z+1\right)\left(xy+y-x-1\right)}=\dfrac{\left(z-1\right)\left(x-1\right)\left(y-1\right)}{\left(z+1\right)\left(x+1\right)\left(y-1\right)}=\dfrac{\left(z-1\right)\left(x-1\right)}{\left(z+1\right)\left(x+1\right)}\\ =\dfrac{\left(5003-1\right)\left(5001-1\right)}{\left(5003+1\right)\left(5001+1\right)}=\dfrac{5002\cdot5000}{5004\cdot5002}=\dfrac{5000}{5004}=\dfrac{1250}{1251}\)