Solve {l}{2z+2y+2x+yz+xz+xy}{(1+x)(1+y)(1+z)}

$$\left. \begin{array} { l } { 2 z + 2 y + 2 x + y z + x z + x y } \\ { ( 1 + x ) ( 1 + y ) ( 1 + z ) } \end{array} \right.$$

Least Common Multiple

$$\left(x+1\right)\left(y+1\right)\left(z+1\right)\left(xy+xz+2x+yz+2y+2z\right)$$

Solution Steps

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$\left(x+1\right)\left(y+1\right)\left(z+1\right)\left(xy+xz+2x+yz+2y+2z\right)$$

Expand the expression.

$$x^{2}y^{2}+x^{2}z^{2}+2x^{2}+xy^{2}z^{2}+3xy^{2}+4xyz^{2}+9xyz+5xy+3xz^{2}+4xzy^{2}+5xz+2x+y^{2}z^{2}+2y^{2}+yx^{2}z^{2}+3yx^{2}+3yz^{2}+4yzx^{2}+5yz+2y+2z^{2}+zx^{2}y^{2}+3zx^{2}+3zy^{2}+2z$$

Evaluate

$$xy+xz+2x+yz+2y+2z,\ \left(x+1\right)\left(y+1\right)\left(z+1\right)$$