Bài giải:

$xy\left( x+y \right)+yz\left( y+z \right)+xz\left( x+z \right)+2xyz$

=$\left[ xy\left( x+y \right)+xyz \right]+\left[ yz\left( y+z \right)+xyz \right]+xz\left( x+z \right)$

=$xy\left( x+y+z \right)+yz\left( y+z+x \right)+xz\left( x+z \right)$

=$y\left( x+y+z \right)\left( x+z \right)+xz\left( x+z \right)$

=$\left( x+z \right)\left[ y\left( x+y+z \right)+xz \right]$

=$\left( x+z \right)\left( xy+{{y}^{2}}+yz+xz \right)$

=$\left( x+z \right)\left[ y\left( x+y \right)+z\left( x+y \right) \right]$

=$\left( x+z \right)\left( x+y \right)\left( y+z \right)$

Đáp án đúng là A