Solve {c}{x^3+y^3+z^3-3xyz}{text{plot}}

$$\left. \begin{array} { c } { x ^ { 3 } + y ^ { 3 } + z ^ { 3 } - 3 x y z } \\ { \text { plot } } \end{array} \right.$$

Least Common Multiple

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

Solution Steps

Factor the expressions that are not already factored.

$$z^{3}+y^{3}-3xyz+x^{3}=\left(x+y+z\right)\left(x^{2}-xy-xz+y^{2}-yz+z^{2}\right)$$

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

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

Expand the expression.

$$loptx^{3}-3loptxyz+lopty^{3}+loptz^{3}$$

Evaluate

$$x^{3}-3xyz+y^{3}+z^{3},\ lopt$$