Cho biểu thức $\Large C=xyz-\left( xy+yz+zx \right)+x+y+z-1$. Phân tíc

Cho biểu thức $\Large C=xyz-\left( xy+yz+zx \right)+x+y+z-1$. Phân tích $\Large C$ thành nhân tử :

• A. $\Large C=\left( z-1 \right)\left( xy-y-x+1 \right)$
• B. $\Large C=\left( z-1 \right)\left( y-1 \right)\left( x+1 \right)$
• C. $\Large C=\left( z-1 \right)\left( y-1 \right)\left( x-1 \right)$
• D. $\Large C=\left( z+1 \right)\left( y-1 \right)\left( x-1 \right)$

$\Large \begin{align}  C&=xyz-xy-yz-zx+x+y+z-1 \\  & =\left( xyz-xy \right)-\left( yz-y \right)-\left( zx-x \right)+\left( z-1 \right) \\  & =xy\left( z-1 \right)-y\left( z-1 \right)-x\left( z-1 \right)+\left( z-1 \right) \\  & =\left( z-1 \right)\left( xy-y-x+1 \right) \\  & =\left( z-1 \right)\left[ y\left( x-1 \right)-\left( x-1 \right) \right] \\  & =\left( z-1 \right)\left( y-1 \right)\left( x-1 \right) \\ \end{align}$